Physics

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momentum

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the measure of an object's translational motion—its tendency to continue moving in a particular direction. Momentum = mass times its velocity.
kg · m/s

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impulse

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a force exerted on it for a certain amount of time.
Force * Time
Although the impulses that transfer momentum involve forces, momentum itself does not.

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Angular momentum

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measure of an object's rotational motion—its tendency to continue spinning about a particular axis. Simply put, your car's angular momentum indicates the direction of its rotation and just how difficult it was to get it spinning with its current angular velocity. The car's angular momentum is its rotational mass times its angular velocity.
kg · m2/s

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angular impulse

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a torque exerted on it for a certain amount of time. The change in your car's angular momentum and is equal to the product of the torque exerted on your car times the duration of that torque.

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Newton's third law of rotational motion:

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if one object exerts a torque on a second object, then the second object will exert an equal but oppositely directed torque on the first object.

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Newton's first law of rotational motion:

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A rigid object that is not wobbling and is not subject to any outside torques rotates at a constant angular velocity, turning equal amounts in equal times about a fixed axis of rotation.

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Newton's second law of rotational motion:

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The torque exerted on an object that is not wobbling is equal to the product of that object's rotational mass times its angular acceleration. The angular acceleration points in the same direction as the torque

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Potential Energy and Acceleration

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An object accelerates in the direction that reduces its total potential energy as quickly as possible

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friction

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a force that opposes the relative motion of two surfaces in contact with one another

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relative motion

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traveling with different velocities so that a person standing still on one surface would observe the other surface as moving. In opposing relative motion, friction exerts forces on both surfaces in directions that tend to bring them to a single velocity.

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sliding friction

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When two surfaces are moving across one another, sliding friction acts to stop them from sliding.
That's why the force of sliding friction is generally weaker than that of static friction and why it's easier to keep the file cabinet moving than it is to get it started.

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static friction

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The forces that resist relative motion as outside forces try to make two touching surfaces begin to slide across one another

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traction

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the largest amount of frictional force that the file cabinet can obtain from the floor at any given moment

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sliding friction does is convert useful, ordered energy. . .

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energy that can easily be used to do work—into relatively useless, disordered energy. This disordered energy is called thermal energy

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power

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the amount of work you do in a certain amount of time, or work/time.
Watt.

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kinetic energy

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is equal to one-half of its mass times the square of its speed. Racing around at twice the speed takes four times the energy.

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rotational motion

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Motion around a fixed point (which prevents translation)

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rotational inertia

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A body that's rotating tends to remain rotating; a body that's not rotating tends to remain not rotating.

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angular position

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describes the seesaw's orientation relative to some reference orientation; it can be specified by determining how far the seesaw has rotated away from its reference orientation and the axis or line about which that rotation has occurred. The seesaw's angular position is a vector quantity of relatively minor importance, pointing along the rotation axis with a magnitude equal to the rotation angle. radian

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Angular velocity

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vector quantity of rotational motion and measures how quickly the seesaw's angular position changes; it consists of the angular speed at which the seesaw is rotating and the axis about which that rotation proceeds.

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angular speed

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A measure of the angle through which an object rotates in a certain amount of time. radian-per-second (abbreviated 1/s)

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axis of rotation

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line in space about which the seesaw is rotating. right-hand rule.

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center of mass

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here's a special point in or near a free object about which all its mass is evenly balanced and about which it naturally spins—its center of mass. The axis of rotation passes right through this point so that, as the free object rotates, the center of mass doesn't move unless the object has an overall translational velocity.
rotational mass also depends on an object's shape, particularly on how far each portion of its ordinary mass is from the axis of rotation.

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Rotational mass

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measure of an object's rotational inertia, its resistance to changes in its angular velocity. An object's rotational mass depends both on its ordinary mass and on how that mass is distributed within the object. The SI unit of rotational mass is the kilogram-meter2 (abbreviated kg · m2).
The larger an object's rotational mass, the more slowly its angular velocity changes in response to a specific torque.

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Torque

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has both a magnitude and a direction. The ball will begin to rotate, acquiring a nonzero angular velocity (Fig. 2.1.7c). The direction of this angular velocity is that of the torque. The SI unit of torque is the newton-meter (abbreviated N · m).
Torque = Rotational Mass * Angular Acceleration.
torque produced by a force is equal to the product of the lever arm times that force, where we include only the component of the force that is perpendicular to the lever arm.

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Angular acceleration

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measures how quickly the seesaw's angular velocity changes. It's analogous to acceleration, which measures how quickly an object's translational velocity changes. Just as with acceleration, angular acceleration involves both a magnitude and a direction. radian-per-second2 (abbreviated 1/s2). angular acceleration is equal to the torque exerted on it divided by its rotational mass.

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lever arm

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The distance from the pivot to the place where you push on the seesaw is called the lever arm; in general, the longer the lever arm, the less force it takes to cause a particular angular acceleration.

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Balanced seesaw:

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meaning that the net torque on it is zero. Although each child's weight exerts a torque on the seesaw, the two torques sum to zero. Since the seesaw experiences zero net torque and no angular acceleration, it continues rotating at constant angular velocity. A balanced seesaw has zero angular acceleration; it's only by unbalancing the seesaw that the children can change the angular velocity of the seesaw.

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Balanced seesaw's angular velocity is constant

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motionless and horizontal

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Observations about Wheels

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frictional force

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The Two Types of Friction

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Sleds and Friction

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A stationary sled

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Static friction (distance traveled is zero)
Sliding friction (distance traveled is nonzero)

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Forms of Energy

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A portion of energy can be:

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Wheels

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Eliminate sliding
friction at roadway

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Summary about Wheels

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Glancing Collisions

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Cars exchange ang. mom. via ang. impulses

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Rotational Mass can Change

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Acceleration and
Potential Energy

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A car on an uneven floor accelerates in whatever
direction reduces its total potential energy as
rapidly as possible

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Rebound energy < collision energy

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Coefficient of Restitution

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Bouncing from an Elastic Floor

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Both ball and floor dent during a bounce

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Bouncing from Moving Surfaces

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Ball and Bat (Part 1)

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Ball and Bat (Part 2)

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Ball and Bat (Part 3)

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Bouncing’s Effects on Objects

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A bouncing ball transfers momentum

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Impact Forces

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Harder surfaces bounce faster

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The Ball’s Effects on a Bat

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Roller Coasters:
The Feeling of Weight

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The Feeling of Acceleration

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Acceleration and Weight

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Carousels (Part 1)

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Carousels
centripetal acceleration

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Roller Coasters (Part 1 –Hills)

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Roller Coasters (Part 2 – Loops)

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Choosing a Seat

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Mass as a Measure

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Weight as a Measure

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Spring Scales 12
Springs
Equilibrium

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Weighing via Equilibrium

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Springs

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Hooke’s Law

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A Spring Scale

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Spring Scales and Acceleration

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Oscillation

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Scales

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- they must be equal in magnitude but opposite in direction so that they sum to zero net force

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restoring force
Hooke's law

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- acts to restore the spring to equilibrium. Second, the spring's restoring force is proportional to how far it has been distorted (stretched or compressed) from its equilibrium length
restoring force = -spring constant x distortion. spring constant = measure of the spring's stiffness

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Hooke's law cont.

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If you distort an object too far, it will usually begin to exert less force than Hooke's law demands. This is because you will have exceeded the elastic limit of the object and will probably have permanently deformed it in the process

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Calibration is the process:

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of comparing a local device or reference to a generally accepted standard to ensure accuracy. To calibrate a spring scale, the device or its reference components must be compared against standard weights.

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As the scale moves:

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You are bouncing up and down because you have excess energy that is shifting back and forth between gravitational potential energy, kinetic energy, and elastic potential energy. This bouncing continues until sliding friction in the scale has converted it all into thermal energy. Only then does the bouncing stop and the scale read your correct weight. ((you reached your peak speed and kinetic energy at the moment you passed through equilibrium)) ((An object at equilibrium is not accelerating, but its velocity may not be zero. If it was moving when it reached equilibrium it will coast at constant velocity.))

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The amount of kinetic energy transformed at impact is called:

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the collision energy

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The total amount of kinetic energy released as the surface and ball push apart is:

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the rebound energy. Collision energy that doesn't reappear as rebound energy has been transformed into thermal energy.

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Coefficient of restitution

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the ratio of its rebound speed to its collision speed when it bounces off a hard, immobile surface. A superball, in contrast, retains about 81% of its original kinetic energy after a bounce
(coefficient of restitution of about 0.90).

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When a ball bounces off a moving surface that's rigid and massive, the ball's coefficient of restitution still applies. But now we must use a more general form of that speed ratio.

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C of R: Speed of sep/Speed of approach.
The baseball's coefficient of restitution is 0.55, so after the collision the speed of separation will be only 0.55 times the speed of approach, or 110 km/h. Bat moving towards pitcher, 100 km/h plus 110 km/h or a total speed of 210 km/h.

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in a number of interesting ways.

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First, as we noted before, the bat rebounds from the ball. The bat decelerates slightly during the collision so that its speed after the impact is a little less than before it. Since the ball's final speed depends on the bat's final speed, a slower bat means a slower ball. When the ball pushes on the bat and makes it accelerate backward, it also exerts a torque on the bat about its center of mass and makes it undergo angular acceleration. (center of percussion, the handle experiences no overall acceleration)

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The ball pushes on the bat during the collision and the bat responds. . .

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Finally, the collision often causes the bat to vibrate. Like a xylophone bar struck by a mallet (Fig. 3.2.7a), the bat bends back and forth rapidly with its ends and center moving in opposite directions (Fig. 3.2.7b). These vibrations sting your hands and can even break a wooden bat. However, near each end of the bat, there's a point that doesn't move when the bat vibrates—a vibrational node. ((Equip manuf have inelastic collisions for bats}}

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As you accelerate forward in a car:

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you feel a gravity-like feeling of acceleration in the direction opposite to the acceleration. This feeling of acceleration is really the mass of your body resisting acceleration.

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Despite the convincing sensations, the backward heavy feeling in your gut as you accelerate forward is the result of inertia and is not due to a real backward force.

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We'll call this experience a feeling of acceleration . It always points in the direction opposite the acceleration that causes it, and its strength is proportional to that acceleration.

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apparent weight

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We'll call your combined experience of weight and feeling of acceleration your apparent weight. The faster you accelerate, the stronger the backward feeling of acceleration and the more your apparent weight points toward the back of the car. When you accelerate forward gently, the backward feeling of acceleration is small and your apparent weight is mostly downward. (b) When you accelerate forward quickly, you experience a strong backward feeling of acceleration and your apparent weight is backward and down. When you're not driving and can safely close your eyes, you should be able to feel acceleration in any direction.

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uniform circular motion

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Motion at a constant speed around a circular trajectory. An object undergoing uniform circular motion is accelerating toward the center of the circle

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centripetal acceleration

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An acceleration of this type, toward the center of a circle, is called a centripetal acceleration and is caused by a centrally directed force, a centripetal force. A centripetal force is not a new, independent type of force like gravity, but the net result of whatever forces act on the object. An acceleration toward the center of a circle is called a centripetal acceleration and is caused by a centrally directed force, a centripetal force. A centripetal force is not a new, independent type of force like gravity, but the net result of whatever forces act on the object.

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uniform circular motion

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“Uniform” means that the boy is always moving at the same speed, although his direction keeps changing. “Circular” describes the path the boy follows as he moves, his trajectory.

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The faster the carousel turns and the larger the radius of the boy's circular trajectory, the more he accelerates. His acceleration is equal to:

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the square of the carousel's angular speed times the radius of his path.

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To experience a 1g feeling of acceleration:

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You must accelerate in the opposite direction at 9.8 m/s2(32 ft/s2), the acceleration due to gravity. If you accelerate 5 times that quickly, on the scrambler or on an airplane maneuvering sharply, you'll experience a 5g feeling of acceleration.

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That feeling of acceleration gives you an apparent weight that's different from your real weight. As we saw with a car, rapid forward acceleration tips your apparent weight backward toward the rear of the vehicle, while rapid deceleration tips it toward the front. But a roller coaster can do something a car can't:

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it can accelerate downward rapidly! In that case, the feeling of acceleration you experience is upward and opposes your downward weight so that they partially cancel. As a result, your apparent weight is less than your real weight and points downward or perhaps, if the downward acceleration is fast enough, points upward.
if you accelerate downward at just the right rate, the upward feeling of acceleration will exactly cancel your downward weight. you will be accelerating downward at 9.8 m/s2(32 ft/s2). You will experience the same sensations as a diver who has just stepped off the high dive.

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However, a roller coaster is attached to a track, and its rate of downward acceleration can actually exceed that of a freely falling object. In those special situations:

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the track will be assisting gravity in pushing the roller coaster downward. As a rider, you will feel less than weightless. The upward feeling of acceleration will be so large that your apparent weight will be in the upward direction, as though the world had turned upside down!

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Roller coaster: the weightless feeling can't last. It occurs only during downward acceleration and disappears as your car levels off near the bottom of the hill. By the time the car begins its rise into the loop-the-loop, it is traveling at maximum speed and has begun to accelerate upward. . .

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This upward acceleration creates a downward feeling of acceleration so that your apparent weight is huge and downward. You feel pressed into your seat as you experience 2 or 3g's.
Halfway up the loop-the-loop, your true acceleration is inward and downward, so the feeling of acceleration you experience is outward and upward (4). Your apparent weight is still much more than your weight and is directed outward. You feel pressed into your seat, and the car itself is pressed against the track

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Finally, you reach the top of the loop-the-loop...

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The car has slowed somewhat as the result of its climb against the force of gravity. But it's still accelerating toward the center of the circle, and you still experience a feeling of acceleration outward and, in this case, upward. Your weight is downward, but the upward feeling of acceleration exceeds your weight. Your apparent weight is upward