Understanding Linear-Rotational Equivalents - AP Physics C Electricity & Magnetism
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What is the rotational equivalent of mass?
What is the rotational equivalent of mass?
The correct answer is moment of inertia. For linear equations, mass is what resists force and causes lower linear accelerations. Similarly, in rotational equations, moment of inertia resists torque and causes lower angular accelerations.
The correct answer is moment of inertia. For linear equations, mass is what resists force and causes lower linear accelerations. Similarly, in rotational equations, moment of inertia resists torque and causes lower angular accelerations.
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In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?
In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?
Just as force causes linear acceleration, torque causes angular acceleration. This can be seen most in the linear-rotational comparison of Newton's second law:
Just as force causes linear acceleration, torque causes angular acceleration. This can be seen most in the linear-rotational comparison of Newton's second law:
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A boot is put in a 
stick which is attached to a rotor. The rotor turns with an angular velocity of 
. What is the linear velocity of the boot?
A boot is put in a
Linear (tangential) velocity, 
is given by the following equation:
Here, 
is the angular velocity in radians per second and 
is the radius in meters.
Solve.
Linear (tangential) velocity,
Here,
Solve.
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A particle is moving at constant speed in a straight line past a fixed point in space, c. How does the angular momentum of the particle about the fixed point in space change as the particle moves from point a to point b?
A particle is moving at constant speed in a straight line past a fixed point in space, c. How does the angular momentum of the particle about the fixed point in space change as the particle moves from point a to point b?
The angular momentum of a particle about a fixed axis is 
. As the particle draws nearer the fixed axis, both 
and 
change. However, the product 
remains constant. If you imagine a triangle connecting the three points, the product 
represents the 
"of closest approach", labeled "
" in the diagram.
The angular momentum of a particle about a fixed axis is
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What is the rotational equivalent of mass?
What is the rotational equivalent of mass?
The correct answer is moment of inertia. For linear equations, mass is what resists force and causes lower linear accelerations. Similarly, in rotational equations, moment of inertia resists torque and causes lower angular accelerations.
The correct answer is moment of inertia. For linear equations, mass is what resists force and causes lower linear accelerations. Similarly, in rotational equations, moment of inertia resists torque and causes lower angular accelerations.
Compare your answer with the correct one above
In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?
In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?
Just as force causes linear acceleration, torque causes angular acceleration. This can be seen most in the linear-rotational comparison of Newton's second law:
Just as force causes linear acceleration, torque causes angular acceleration. This can be seen most in the linear-rotational comparison of Newton's second law:
Compare your answer with the correct one above
A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of . What is the linear velocity of the boot?
A boot is put in a
Linear (tangential) velocity, is given by the following equation:
Here, is the angular velocity in radians per second and is the radius in meters.
Solve.
Linear (tangential) velocity,
Here,
Solve.
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A particle is moving at constant speed in a straight line past a fixed point in space, c. How does the angular momentum of the particle about the fixed point in space change as the particle moves from point a to point b?
A particle is moving at constant speed in a straight line past a fixed point in space, c. How does the angular momentum of the particle about the fixed point in space change as the particle moves from point a to point b?
The angular momentum of a particle about a fixed axis is . As the particle draws nearer the fixed axis, both and change. However, the product remains constant. If you imagine a triangle connecting the three points, the product represents the "of closest approach", labeled "" in the diagram.
The angular momentum of a particle about a fixed axis is
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