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31 Cards in this Set
- Front
- Back
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Newton's First Law
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A body moves with constant velocity (which may be zero) unless acted on by a force<br><br>-defines 0 force<br>-gives inertial frame
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A body moves with constant velocity (which may be zero) unless acted on by a force<br><br>-defines 0 force<br>-gives inertial frame
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Newton's First Law
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Newton's Second Law
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The time rate of change of the momentum of a body equals the force acting on the bodyThe acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass m of the body, i.e., F = ma<br><br>-defines nonzero force<br><$> \tiny F=ma</$> if m is constant and<$> a=dv/dt</$><br>-holds only in the inertial frame defined by the first law /
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The time rate of change of the momentum of a body equals the force acting on the bodyThe acceleration a of a body is parallel and directly proportional to the net force F acting on the body, is in the direction of the net force, and is inversely proportional to the mass m of the body, i.e., F = ma<br><br>-defines nonzero force<br><$> \tiny F=ma</$> if m is constant and<$> a=dv/dt</$><br>-holds only in the inertial frame defined by the first law /
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Newton's Second Law
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Tension
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force that a rope exerts when it is pulled on<br><br>every piece of the rope feels tension in both directions except the end points, which feel a tension on one side and a force on the other side from whatever object is attached to that end
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force that a rope exerts when it is pulled on<br><br>every piece of the rope feels tension in both directions except the end points, which feel a tension on one side and a force on the other side from whatever object is attached to that end
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Tension
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Normal force
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force perpendicular to asurface that the surface applies to an object<br><br>total force applied by a surface is usually a combination of the normal force and the friction force<br><br>for frictionless surfaces, only the normal force exists<br><br>comes about because the surface actually compresses a tiny bit and acts like a very rigid spring- surface is squashed unti lthe restoring force equals the force necessary to keep the object from squashing in any more<br><br>only dif bw tension & normal force is the direction (both modeled by a spring; tension is stretched, normal is compressed)<br><br>compressive tension is another name for normal force
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force perpendicular to asurface that the surface applies to an object<br><br>total force applied by a surface is usually a combination of the normal force and the friction force<br><br>for frictionless surfaces, only the normal force exists<br><br>comes about because the surface actually compresses a tiny bit and acts like a very rigid spring- surface is squashed unti lthe restoring force equals the force necessary to keep the object from squashing in any more<br><br>only dif bw tension & normal force is the direction (both modeled by a spring; tension is stretched, normal is compressed)<br><br>compressive tension is another name for normal force
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Normal force
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Friction
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the force parallel to a surface that a surface applies to an object<br>2 types:<br>1. kinetic friction: 2 objects moving relative to each other (proportional to normal force,<$>F= \mu_k N</$> )<br>2. static friction:2 objects at rest relative to each other (<$> F \leq \mu_s N </$>)
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the force parallel to a surface that a surface applies to an object<br>2 types:<br>1. kinetic friction: 2 objects moving relative to each other (proportional to normal force,<$>F= \mu_k N</$> )<br>2. static friction:2 objects at rest relative to each other (<$> F \leq \mu_s N </$>)
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Friction
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Vectors
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have length and direction- unlike points, their starting location doesn't matter<br><br>"a command to move"<br><br>coordinates don't depend on the origin<br><br>similar but different notation than that of points<br><br>if you want points instead of vectors, must specify origin
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have length and direction- unlike points, their starting location doesn't matter<br><br>"a command to move"<br><br>coordinates don't depend on the origin<br><br>similar but different notation than that of points<br><br>if you want points instead of vectors, must specify origin
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Vectors
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Dot product (Geometrical definition)
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<$>\vec a \cdot\vec b = |a| \cdot |b| cos \theta_{ab} </$> where <$>|a| </$>is the length of <$>\vec a </$>and <$>\theta </$>
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<$>\vec a \cdot\vec b = |a| \cdot |b| cos \theta_{ab} </$> where <$>|a| </$>is the length of <$>\vec a </$>and <$>\theta </$>
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Dot product (Geometrical definition)
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Dot Product (Cartesian Definition)
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<$>\vec a \cdot \vec b = a_xb_x + a_yb_y </$>
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<$>\vec a \cdot \vec b = a_xb_x + a_yb_y </$>
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Dot Product (Cartesian Definition)
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trajectory
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mathematical description of where something is as a function of time
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mathematical description of where something is as a function of time
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trajectory
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number of degrees of freedom
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how many # you need to keep track of for your experiment
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how many # you need to keep track of for your experiment
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number of degrees of freedom
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Newton's Third Law
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For every force on one body, there is an equal and opposite force on another body<br><$>F_1 = -F_2</$><br><br>-postulates the conservation of momentum (though sometimes momentum can be carried off by a field)<br>-says we will never find a paricle accelerating unless there's some other particle accelerating somewhere else<br><br>
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For every force on one body, there is an equal and opposite force on another body<br><$>F_1 = -F_2</$><br><br>-postulates the conservation of momentum (though sometimes momentum can be carried off by a field)<br>-says we will never find a paricle accelerating unless there's some other particle accelerating somewhere else<br><br>
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Newton's Third Law
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inertial frame
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reference frame in which Newton's first Law holds true<br><br>-state what frame you are measuring the velocity relative to<br><br>-really a frame that moves with a constant velocity with respect to something
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reference frame in which Newton's first Law holds true<br><br>-state what frame you are measuring the velocity relative to<br><br>-really a frame that moves with a constant velocity with respect to something
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inertial frame
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momentum conservation
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<$> dp_total / dt = 0</$>
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<$> dp_total / dt = 0</$>
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momentum conservation
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"static" setup
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all the objects are motionless<br>-F=ma tells then the total external foce acting on the object must be zero<br>-converse isn't true (could be constant nonzero velocity)<br><br>-goal is to find various forces so that there is zero net force/torque on each object<br>1.break force vector into components
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How to define a inertial frame
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give a constant velocity with respect to another frame (like the origin)<br><br>Newton's first law must hold true in it (a body moves with constant velocity unless acted on by a force)
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free body diagram
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diagram with all the forces drawn out
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How to solve for position and velocity given a force
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solve differential equation<br><br><$>F=ma=m\stackrel{..}{x}</$>
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How to find force given a physical situation
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use a free body diagram<br>write all the F=ma eqns they imply <br>solve resulting system of linear equations
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