What is the angular acceleration of a system in rotational equilibrium?

It is zero , because the net torque exerted on the system is zero.

State the principle of torques .

For a system in rotational equilibrium, the sum of the clockwise torques equals the sum of the counterclockwise torques.

How is a balanced beam problem solved?

Identify the location of the pivot and calculate the torque due to each force about it Sum the clockwise and counterclockwise torques separately Use the principle of torques to calculate the unknown quantity

Rotational equilibrium is analogous to .......... equilibrium.

Rotational equilibrium is analogous to translational equilibrium.

True or False? A system in rotational equilibrium must be at rest.

False. The system may also rotate with a constant angular velocity , because the net torque is zero and there is no angular acceleration.

State Newton's first law in rotational form.

If the net torque exerted on a system is zero , the angular velocity of that system remains constant .

If the net torque exerted on a system is zero, the system is said to be in .......... equilibrium.

If the net torque exerted on a system is zero, the system is said to be in rotational equilibrium.

True or False? A non-rotating system cannot have a constant angular velocity.

False. A constant angular velocity can be an angular velocity of zero , when the system is not rotating.

What happens to the angular velocity of a rigid system if the torques exerted on it are not balanced ?

The angular velocity changes , because a net torque produces an angular acceleration .

What determines the direction of the angular acceleration of a rigid system?

The direction of the net torque .

State Newton's second law in rotational form.

The angular acceleration of a rigid system is directly proportional to the net torque exerted on it and is in the same direction .

In a pulley-mass system, what exerts the torque on the pulley?

The tension in the string, acting at the radius of the pulley.

Unbalanced torques produce .......... acceleration.

Unbalanced torques produce angular acceleration.

True or False? A larger rotational inertia gives a larger angular acceleration for the same net torque.

False. Angular acceleration is inversely proportional to rotational inertia, so a larger rotational inertia gives a smaller angular acceleration.

Why may linear and rotational quantities need to be calculated separately for a pulley-mass system?

Torques and linear forces act independently on the system.

AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 5: Torque & Rotational DynamicsNewton’s First & Second Law in Rotational Form

Newton’s First & Second Law in Rotational Form (College Board AP® Physics 1: Algebra-Based): Flashcards

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FrontRotational Equilibrium
Define rotational equilibrium.

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Cards in this collection (20)

Define rotational equilibrium.
Rotational equilibrium is a configuration of torques such that the net torque exerted on the system is zero.
$\sum τ_{i} = 0$
What is the angular acceleration of a system in rotational equilibrium?
It is zero, because the net torque exerted on the system is zero.
State the principle of torques.
For a system in rotational equilibrium, the sum of the clockwise torques equals the sum of the counterclockwise torques.
How is a balanced beam problem solved?
- Identify the location of the pivot and calculate the torque due to each force about it
- Sum the clockwise and counterclockwise torques separately
- Use the principle of torques to calculate the unknown quantity
Rotational equilibrium is analogous to .......... equilibrium.
Rotational equilibrium is analogous to translational equilibrium.
True or False?
A system in rotational equilibrium must be at rest.
False.
The system may also rotate with a constant angular velocity, because the net torque is zero and there is no angular acceleration.
State Newton's first law in rotational form.
If the net torque exerted on a system is zero, the angular velocity of that system remains constant.
If the net torque exerted on a system is zero, the system is said to be in .......... equilibrium.
If the net torque exerted on a system is zero, the system is said to be in rotational equilibrium.
True or False?
A non-rotating system cannot have a constant angular velocity.
False.
A constant angular velocity can be an angular velocity of zero, when the system is not rotating.
What happens to the angular velocity of a rigid system if the torques exerted on it are not balanced?
The angular velocity changes, because a net torque produces an angular acceleration.
What determines the direction of the angular acceleration of a rigid system?
The direction of the net torque.
How do you find the net torque from clockwise and counterclockwise torques?
Subtract one total from the other:
$\sum τ = τ_{clockwise} - τ_{counterclockwise}$
The net torque acts in the direction of the larger total.
State Newton's second law in rotational form.
The angular acceleration of a rigid system is directly proportional to the net torque exerted on it and is in the same direction.
State the equation for the angular acceleration of a system.
$α_{sys} = \frac{\sum τ}{I_{sys}} = \frac{τ_{net}}{I_{sys}}$
- $α_{sys}$ = angular acceleration of the system (rad/s²)
- $τ_{net}$ = net torque exerted on the system (N·m)
- $I_{sys}$ = rotational inertia of the system (kg·m²)
In a pulley-mass system, what exerts the torque on the pulley?
The tension in the string, acting at the radius of the pulley.
What is the rotational analog of mass in Newton's second law?
Rotational inertia, $I$ .
$F_{net} = m a$ becomes $τ_{net} = I α$
Unbalanced torques produce .......... acceleration.
Unbalanced torques produce angular acceleration.
True or False?
A larger rotational inertia gives a larger angular acceleration for the same net torque.
False.
Angular acceleration is inversely proportional to rotational inertia, so a larger rotational inertia gives a smaller angular acceleration.
State the relationships between tangential and angular motion.
$v_{T} = r ω$
$a_{T} = r α$
- $v_{T}$ = tangential velocity (m/s)
- $a_{T}$ = tangential acceleration (m/s²)
- $r$ = distance from the axis of rotation (m)
- $ω$ = angular velocity (rad/s)
- $α$ = angular acceleration (rad/s²)
Why may linear and rotational quantities need to be calculated separately for a pulley-mass system?
Torques and linear forces act independently on the system.

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