A fixed 0.15 kg solid-disk pulley with a radius of 0.075 m is acted on by a net torque of 6.8 m·N. What is the angular acceleration of the pulley?
To find the angular acceleration of the pulley, we need to use the formula for torque:
Torque = Moment of Inertia × Angular Acceleration
First, let's find the moment of inertia of the solid disk. The moment of inertia for a solid disk rotating about its axis is given by the equation:
Moment of Inertia = (1/2) × Mass × Radius^2
Given:
Mass of the solid disk = 0.15 kg
Radius of the solid disk = 0.075 m
Plugging in the values, we have:
Moment of Inertia = (1/2) × 0.15 kg × (0.075 m)^2
Now, we can substitute the known values into the equation for torque and solve for angular acceleration:
6.8 m·N = ((1/2) × 0.15 kg × (0.075 m)^2) × Angular Acceleration
We can rearrange this equation to solve for angular acceleration:
Angular Acceleration = (6.8 m·N) / ((1/2) × 0.15 kg × (0.075 m)^2)
Now, let's calculate the angular acceleration.
angular acceleration =
(Torque)/(Moment of inertia)
For a solid disc,
Moment of Inertia = (1/2) M R^2
The answer will be in radians/second^2