Understanding Linear-Rotational Equivalents - AP Physics C: Electricity and Magnetism

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Question

What is the rotational equivalent of mass?

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Answer

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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Question

In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?

Tap to reveal answer

Answer

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:

$\tau=I\alpha$

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Question

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Tap to reveal answer

Answer

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

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Question

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?

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Answer

The angular momentum of a particle about a fixed axis is $\small L=mvr\cos(\theta )$ . As the particle draws nearer the fixed axis, both $\small r$ and $\theta$ change. However, the product $r\cos( \theta)$ remains constant. If you imagine a triangle connecting the three points, the product $r\cos( \theta)$ represents the "of closest approach", labeled "" in the diagram.

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Question

What is the rotational equivalent of mass?

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?

Tap to reveal answer

Answer

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:

$\tau=I\alpha$

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Question

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Tap to reveal answer

Answer

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

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Question

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?

Tap to reveal answer

Answer

The angular momentum of a particle about a fixed axis is $\small L=mvr\cos(\theta )$ . As the particle draws nearer the fixed axis, both $\small r$ and $\theta$ change. However, the product $r\cos( \theta)$ remains constant. If you imagine a triangle connecting the three points, the product $r\cos( \theta)$ represents the "of closest approach", labeled "" in the diagram.

← Didn't Know|Knew It →

Question

What is the rotational equivalent of mass?

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?

Tap to reveal answer

Answer

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:

$\tau=I\alpha$

← Didn't Know|Knew It →

Question

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Tap to reveal answer

Answer

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

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Question

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?

Tap to reveal answer

Answer

The angular momentum of a particle about a fixed axis is $\small L=mvr\cos(\theta )$ . As the particle draws nearer the fixed axis, both $\small r$ and $\theta$ change. However, the product $r\cos( \theta)$ remains constant. If you imagine a triangle connecting the three points, the product $r\cos( \theta)$ represents the "of closest approach", labeled "" in the diagram.

← Didn't Know|Knew It →

Question

What is the rotational equivalent of mass?

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?

Tap to reveal answer

Answer

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:

$\tau=I\alpha$

← Didn't Know|Knew It →

Question

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Tap to reveal answer

Answer

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

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Question

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?

Tap to reveal answer

Answer

The angular momentum of a particle about a fixed axis is $\small L=mvr\cos(\theta )$ . As the particle draws nearer the fixed axis, both $\small r$ and $\theta$ change. However, the product $r\cos( \theta)$ remains constant. If you imagine a triangle connecting the three points, the product $r\cos( \theta)$ represents the "of closest approach", labeled "" in the diagram.

← Didn't Know|Knew It →

Question

What is the rotational equivalent of mass?

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

In rotational kinematics equations, what quantity is analogous to force in linear kinematics equations?

Tap to reveal answer

Answer

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:

$\tau=I\alpha$

← Didn't Know|Knew It →

Question

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Tap to reveal answer

Answer

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

The angular momentum of a particle about a fixed axis is $\small L=mvr\cos(\theta )$ . As the particle draws nearer the fixed axis, both $\small r$ and $\theta$ change. However, the product $r\cos( \theta)$ remains constant. If you imagine a triangle connecting the three points, the product $r\cos( \theta)$ represents the "of closest approach", labeled "" in the diagram.

← Didn't Know|Knew It →

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Understanding Linear-Rotational Equivalents - AP Physics C: Electricity and Magnetism

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.

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:

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?

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.

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.

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.

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:

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?

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.

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.

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.

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:

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?

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.

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.

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.

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:

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?

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.

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.

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.

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:

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?

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.

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.

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:

$\tau=I\alpha$

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

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:

$\tau=I\alpha$

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

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:

$\tau=I\alpha$

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

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:

$\tau=I\alpha$

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$

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:

$\tau=I\alpha$

A boot is put in a stick which is attached to a rotor. The rotor turns with an angular velocity of $30\pi $\frac{rad}{s}$$ . What is the linear velocity of the boot?

Linear (tangential) velocity, is given by the following equation:

Here, $\omega$ is the angular velocity in radians per second and is the radius in meters.

Solve.

$\omega = 30\pi $\frac{rad}{s}$$

$\omega = 30\pi$\frac{m}{s}$$