What four factors determine the magnitude of an object's angular momentum about a reference point?

The distance between the reference point and the object The mass of the object The linear speed of the object The angle between the radial distance and the velocity

A particle moving along a line that passes through the axis has .......... angular momentum about that axis.

A particle moving along a line that passes through the axis has zero angular momentum about that axis.

True or False? A particle moving in a straight line has no angular momentum.

False. It has angular momentum about any axis that its line of motion does not pass through, because it would cause rotation about that axis.

Define angular impulse .

Angular impulse is the product of the average torque exerted on an object or rigid system and the time interval over which it acts.

What is the direction of angular impulse ?

The same direction as the net torque exerted on the object or system.

Angular impulse is the rotational analog of .......... impulse.

Angular impulse is the rotational analog of linear impulse.

For a fixed time interval, a .......... torque produces a greater change in angular momentum.

For a fixed time interval, a larger torque produces a greater change in angular momentum.

What does Newton's first law state in terms of angular momentum ?

The angular momentum of an object or system remains constant unless an external net torque acts on it.

What two quantities are equal to the area under a torque-time graph ?

The angular impulse delivered to the system by the torque The change in angular momentum of the system, when the graph shows the net torque

On a torque-time graph, an area below the time axis represents a .......... angular impulse.

On a torque-time graph, an area below the time axis represents a negative angular impulse.

True or False? A horizontal section of an angular momentum-time graph means the net torque is zero.

True. The slope is zero, so the angular momentum is not changing and the net torque is zero.

AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 6: Energy & Momentum of Rotating SystemsAngular Momentum & Angular Impulse

Angular Momentum & Angular Impulse (College Board AP® Physics 1: Algebra-Based): Flashcards

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FrontAngular Momentum
State the equation for the angular momentum of a rigid system.
BackAngular Momentum
$L = I ω$
$L$ = angular momentum (kg·m²/s)
$I$ = rotational inertia (kg·m²)
$ω$ = angular velocity (rad/s)
BackAngular Momentum
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FrontAngular Momentum
State the equation for the angular momentum of a particle moving perpendicular to its distance from the axis.
BackAngular Momentum
$L = m v r$
$m$ = mass of the particle (kg)
$v$ = linear speed of the particle (m/s)
$r$ = distance between the reference point and the particle (m)
FrontAngular Momentum
State the equation for the angular momentum of a particle when its velocity is not perpendicular to its distance from the axis.
BackAngular Momentum
$L = m v r sin θ$
$θ$ = angle between the distance $r$ and the velocity $v$ (rad)

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Cards in this collection (25)

State the equation for the angular momentum of a rigid system.
$L = I ω$
- $L$ = angular momentum (kg·m²/s)
- $I$ = rotational inertia (kg·m²)
- $ω$ = angular velocity (rad/s)
State the equation for the angular momentum of a particle moving perpendicular to its distance from the axis.
$L = m v r$
- $m$ = mass of the particle (kg)
- $v$ = linear speed of the particle (m/s)
- $r$ = distance between the reference point and the particle (m)
State the equation for the angular momentum of a particle when its velocity is not perpendicular to its distance from the axis.
$L = m v r sin θ$
- $θ$ = angle between the distance $r$ and the velocity $v$ (rad)
Which two equations combine to give $L = m v r$ for a particle?
- $I = m r^{2}$
- $ω = \frac{v}{r}$
Substituting into $L = I ω$ gives $L = (m r^{2}) (\frac{v}{r}) = m v r$
What four factors determine the magnitude of an object's angular momentum about a reference point?
- The distance between the reference point and the object
- The mass of the object
- The linear speed of the object
- The angle between the radial distance and the velocity
A particle moving along a line that passes through the axis has .......... angular momentum about that axis.
A particle moving along a line that passes through the axis has zero angular momentum about that axis.
True or False?
A particle moving in a straight line has no angular momentum.
False.
It has angular momentum about any axis that its line of motion does not pass through, because it would cause rotation about that axis.
Define angular impulse.
Angular impulse is the product of the average torque exerted on an object or rigid system and the time interval over which it acts.
State the equation for angular impulse.
$angular impulse = τ ∆ t$
- $τ$ = average torque (N·m)
- $∆ t$ = time interval (s)
What is the unit of angular impulse?
$N·m·s$
What is the direction of angular impulse?
The same direction as the net torque exerted on the object or system.
Angular impulse is the rotational analog of .......... impulse.
Angular impulse is the rotational analog of linear impulse.
True or False?
A system can receive angular impulse even if the average torque on it is zero.
False.
When the average torque over the time interval is zero, no angular impulse is exerted, since angular impulse = $τ ∆ t$ .
State the impulse-momentum theorem in rotational form.
The angular impulse exerted on an object or rigid system is equal to its change in angular momentum.
$angular impulse = ∆ L = τ ∆ t$
- $∆ L$ = change in angular momentum (kg·m²/s)
- $τ$ = torque exerted on the system (N·m)
- $∆ t$ = time interval (s)
State the form of the impulse-momentum theorem that is most useful in calculations.
$∆ L = τ ∆ t = I (ω - ω_{0})$
- $I$ = rotational inertia (kg·m²)
- $ω$ = final angular velocity (rad/s)
- $ω_{0}$ = initial angular velocity (rad/s)
For a fixed time interval, a .......... torque produces a greater change in angular momentum.
For a fixed time interval, a larger torque produces a greater change in angular momentum.
What does Newton's first law state in terms of angular momentum?
The angular momentum of an object or system remains constant unless an external net torque acts on it.
State Newton's second law in terms of angular momentum.
The rate of change of angular momentum is equal to the net external torque exerted on an object or system.
$τ = \frac{∆ L}{∆ t}$
- $τ$ = net torque (N·m)
- $∆ L$ = change in angular momentum (kg·m²/s)
- $∆ t$ = time interval (s)
When can $τ = \frac{∆ L}{∆ t}$ be used but $τ_{net} = I α$ cannot?
When the rotational inertia of the body is not constant.
True or False?
A small torque acting for a long time can change angular momentum as much as a large torque acting for a short time.
True.
The change in angular momentum depends on the angular impulse $τ ∆ t$ , so different combinations of torque and time can give the same value.
What two quantities are equal to the area under a torque-time graph?
- The angular impulse delivered to the system by the torque
- The change in angular momentum of the system, when the graph shows the net torque
What is the unit of the area under a torque-time graph?
$N·m·s$
On a torque-time graph, an area below the time axis represents a .......... angular impulse.
On a torque-time graph, an area below the time axis represents a negative angular impulse.
How is the average net torque found from an angular momentum-time graph?
Calculate the slope of the graph over the time interval.
$τ_{net} = \frac{L_{2} - L_{1}}{t_{2} - t_{1}} = \frac{∆ L}{∆ t}$
True or False?
A horizontal section of an angular momentum-time graph means the net torque is zero.
True.
The slope is zero, so the angular momentum is not changing and the net torque is zero.

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