Angular Acceleration of a Pulley

In summary, the angular acceleration of a pulley is a measure of how quickly the pulley's rotational speed is changing. It is affected by factors such as applied torque, moment of inertia, and friction. Angular acceleration is different from linear acceleration and is calculated using the formula α = τ/I. It is also directly proportional to both angular velocity and time.
  • #1
Cheddar
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Homework Statement


A cable is around a pulley with:
radius = 0.1 m
moment of inertia = 0.15 kg * m(squared)

The cable receives a pull of:
force = 12 N

Find the magnitude of the resulting angular acceleration of the puller.

Homework Equations



Average angular acceleration = Change in angular velocity / Elapsed time
Average angular velocity = Angular displacement / Elapsed time

The Attempt at a Solution



I'm completely stuck since none of the given information can be used in the equations listed above.
 
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  • #2
Hint: Consider Newton's 2nd law for rotation.
 
  • #3
Thanks, I think I have it. So:
angular acceleration = 12 * 0.10 / 0.15 = 8.0 rad/s(squared)
?
 
  • #4
You got it.
 

What is angular acceleration of a pulley?

The angular acceleration of a pulley is a measure of how quickly the pulley is changing its rotational speed. It is usually denoted by the symbol α (alpha) and is measured in radians per second squared.

What factors affect the angular acceleration of a pulley?

The angular acceleration of a pulley is affected by several factors, including the applied torque, the moment of inertia of the pulley, and the friction between the pulley and the axle or rope. The direction and magnitude of the applied torque can also impact the angular acceleration.

How is angular acceleration of a pulley different from linear acceleration?

Angular acceleration is a measure of how quickly the rotational velocity of a pulley changes, while linear acceleration is a measure of how quickly an object's linear velocity changes. Angular acceleration is measured in radians per second squared, while linear acceleration is measured in meters per second squared.

What is the formula for calculating angular acceleration of a pulley?

The formula for calculating angular acceleration of a pulley is α = τ/I, where α is the angular acceleration, τ is the applied torque, and I is the moment of inertia of the pulley. This formula assumes that there is no friction between the pulley and the axle or rope.

How is angular acceleration of a pulley related to angular velocity and time?

Angular acceleration is directly proportional to both angular velocity and time. This means that if the angular velocity increases, the angular acceleration will also increase, and if the time interval over which the acceleration occurs is longer, the angular acceleration will be smaller.

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