A fixed 0.16 kg solid-disk pulley with a radius of 0.070 m is acted on by a net torque of 5.0 m * N. What is the angular acceleration of the pulley?
To find the angular acceleration of the pulley, we can use the equation:
Net Torque = Moment of Inertia * Angular Acceleration
First, we need to find the moment of inertia of the solid disk pulley. The moment of inertia for a solid disk rotating about its axis can be calculated using the formula:
Moment of Inertia (I) = (1/2) * m * r^2
where m is the mass of the pulley and r is the radius of the pulley.
Given:
Mass of the pulley (m) = 0.16 kg
Radius of the pulley (r) = 0.070 m
Substituting these values into the moment of inertia formula, we have:
I = (1/2) * 0.16 kg * (0.070 m)^2
Next, we can substitute the values of the net torque (5.0 m * N) and the moment of inertia (I) into the formula:
Net Torque = Moment of Inertia * Angular Acceleration
5.0 m * N = I * Angular Acceleration
Now, we need to rearrange the equation to solve for the angular acceleration:
Angular Acceleration = Net Torque / Moment of Inertia
Plugging in the values, we have:
Angular Acceleration = 5.0 m * N / ((1/2) * 0.16 kg * (0.070 m)^2)
Calculating this expression will give us the angular acceleration of the pulley.