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Define angular displacement.

The angle in radians through which an object rotates around an axis.

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Define angular displacement.

The angle in radians through which an object rotates around an axis.

Define average angular velocity.

The rate at which angular position changes with time.

Define average angular acceleration.

The rate at which angular velocity changes with time.

What are the units for angular velocity?

Radians per second (rad/s).

What are the units for angular acceleration?

Radians per second squared (rad/s²).

What is the formula to calculate average angular velocity?

ωavg=ΔθΔt\omega_{avg} = \frac{\Delta \theta}{\Delta t} where ωavg\omega_{avg} = average angular velocity, Δθ\Delta \theta = change in angular displacement and Δt\Delta t = change in time.

What is the formula to calculate average angular acceleration?

αavg=ΔωΔt\alpha_{avg} = \frac{\Delta \omega}{\Delta t} where αavg\alpha_{avg} = average angular acceleration, Δω\Delta \omega = change in angular velocity and Δt\Delta t = change in time.

Give the formula relating angular displacement, initial angular displacement, initial angular velocity, angular acceleration, and time.

θ=θ0+ω0t+12αt2\theta = \theta_0 + \omega_0 t + \frac{1}{2} \alpha t^2 where θ\theta = angular displacement at time tt, θ0\theta_0 = initial angular displacement, ω0\omega_0 = initial angular velocity and α\alpha = angular acceleration.

Give the formula relating final angular velocity, initial angular velocity, angular acceleration, and angular displacement.

ω2=ω02+2α(θθ0)\omega^2 = \omega_0^2 + 2\alpha(\theta - \theta_0) where ω\omega = angular velocity at angular displacement θ\theta, ω0\omega_0 = initial angular velocity, α\alpha = angular acceleration and θ0\theta_0 = initial angular displacement.

What is the effect of applying a constant frictional torque to a rotating disk?

The disk experiences angular deceleration and eventually comes to rest.

What is the effect of a constant angular acceleration on an object initially at rest?

The object's angular velocity increases linearly with time.

What is the effect of increasing the radius of a rotating object (while keeping mass and angular velocity constant) on its moment of inertia?

The moment of inertia increases.

What is the effect of increasing angular velocity on angular displacement?

For a given time interval, the angular displacement increases.

What happens if the angular acceleration is zero?

The angular velocity remains constant.