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25 Cards in this Set
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rigid bodies

A rigid body is an object that retains its overall shape, meaning that the particles that make up the rigid body stay in the same position relative to one another. A pool ball is one example


center of mass

is the point about which all the matter in the object is evenly distributed. A net force acting on the object will accelerate it in just the same way as if all the mass of the object were concentrated in its center of mass.


axis of rotation

The rotational motion of a rigid body occurs when every point in the body moves in a circular path around a line called the axis of rotation,


Value in degrees Value in radians

30 π/6
45 π/4 60 π/3 90 π/2 180 π 360 2π 

length of an arc

P = 2πr, and we know that there are 2π radians in a circle. If we wanted to know the length, l, of the arc described by any angle , we would know that this arc is a fraction of the perimeter, (/2π)P. Because P = 2πr, the length of the arc would be:


angular velocity

rate at wich the angle is changing
rad/s 

angular acceleration

rate at which ang. velocity changes over time
rad/s^2 

direction of a rigid body’s angular acceleration

if the magnitude of the angular velocity is increasing, the angular acceleration is in the same direction as the angular velocity vector. On the other hand, if the magnitude of the angular velocity is decreasing, then the angular acceleration points in the direction opposite the angular velocity vector.


torque

effect of force on rotational motion
, if a net force is applied to a point other than the center of mass, it will affect the object’s rotation torque is the product of the applied force and the component of the length of the lever arm that runs perpendicular to the applied force a vector quantity 

maximize torque

Maximize the magnitude of the force, F, that you apply to the lever.
Maximize the distance, r, from the axis of rotation of the point on the lever to which you apply the force. Apply the force in a direction perpendicular to the lever. FrsinO O is the angle made between the vector for the applied force and the lever. 

newtons 1st law and torque

If the net torque acting on a rigid object is zero, it will rotate with a constant angular velocity.
The most significant application of Newton’s First Law in this context is with regard to the concept of equilibrium. When the net torque acting on a rigid object is zero, and that object is not already rotating, it will not begin to rotate. 

newtons 2nd law and torque

the angular acceleration of a body is proportional to the torque applied to it.
force is also proportional to mass, and there is also a rotational equivalent for mass: the moment of inertia, I, which represents an object’s resistance to being rotated torque net=inertia*ang acc 

moment of inertia

mass determines ease of spinning
distribution of a body’s mass has a great effect on its potential for rotation... will rotate more easily if its mass is concentrated near the axis of rotation. ring=mr^2 disk=1/2MR^2 

what moves gets speed faster.. rolling or sliding objects?

an object rolling down an incline will pick up speed more slowly than an object sliding down a frictionless incline. Rolling objects pick up speed more slowly because only some of the kinetic energy they gain is converted into translational motion, while the rest is converted into rotational motion.


conseervation of mechanical energy

Because the wheel loses no energy to friction, we can apply the law of conservation of mechanical energy. The change in the wheel’s potential energy is –mgh. and the wheel’s kinetic energy.


which way is angular momentum pointing?

The angular momentum vector always points in the same direction as the angular velocity vector.


law of conservation of angular momentum and newtons 2nd

the net torque acting on an object is equal to the rate of change of the object’s angular momentum with time
If the net torque action on a rigid body is zero, then the angular momentum of the body is constant or conserved. 

circular motion and newton's first law

that objects moving in a circle—whether they’re tetherballs or planets—are under the constant influence of a changing force, since their trajectory is not in a straight line.


uniform circular motion

leave aside gravity for the moment, the only force acting on the ball is the force of tension, T, of the string. This force is always directed radially inward along the string, toward your hand
Note that although the direction of the ball’s velocity changes, the ball’s velocity is constant in magnitude and is always tangent to the circle. 

centripetal acceleration

The acceleration of a body experiencing uniform circular motion is always directed toward the center of the circle,
Latin word meaning “centerseeking.” We define the centripetal acceleration of a body moving in a circle as: a=v^2/r constant in magnitude but changes in direction always perpendicular to the velocity vector, 

centripetal force

The vector for this force is of constant magnitude, and always points radially inward to the center of the circle, perpendicular to the velocity vector.
We can use Newton’s Second Law and the equation for centripetal acceleration to write an equation that maintains an object’s circular motion: f=ma=mv^2/r The tension in the rope is what provides the centripetal force 

gravitational potential energy

depends on how high an object is off the ground: the higher an object is, the more work needs to be done to get it there.
not an absolute measure amount of work needed to move an object from some arbitrarily chosen reference point to the position it is presently in. 

keplers first law

the path of each planet around the sun is an ellipse with the sun at one focus.


keplers second law

if a line is drawn from the sun to the orbiting planet, then the area swept out by this line in a given time interval is constant. This means that when the planet is farthest from the sun it moves much more slowly than when it is closest to the sun.


keplers third law

states that given the period, T, and semimajor axis, a, of a planet’s elliptical orbit, the ratio T 2/a3 is the same for every planet. The semimajor axis is the longer one, along which the two foci are located.
