A fixed 0.15 kg solid-disk pulley with a radius of 0.065 m is acted on by a net torque of 5.2 m·N. What is the angular acceleration of the pulley?
To find the angular acceleration of the pulley, we can use the formula:
Torque = Moment of Inertia × Angular Acceleration
Where:
Torque is the net torque acting on the pulley (given as 5.2 m·N)
Moment of Inertia is a property of the pulley that measures its resistance to rotational motion
Angular Acceleration is the rate at which the pulley's angular velocity is changing
The moment of inertia of a solid disk can be calculated using the formula:
Moment of Inertia (I) = (1/2) × mass × radius^2
Given that the mass of the pulley is 0.15 kg and the radius is 0.065 m:
I = (1/2) × 0.15 kg × (0.065 m)^2 = 0.000328125 kg·m^2
Now we have all the values to calculate the angular acceleration:
5.2 m·N = 0.000328125 kg·m^2 × Angular Acceleration
Dividing both sides of the equation by 0.000328125 kg·m^2 gives us:
Angular Acceleration = 5.2 m·N / 0.000328125 kg·m^2
Calculating the division:
Angular Acceleration ≈ 15829.27 rad/s^2
Therefore, the angular acceleration of the pulley is approximately 15829.27 rad/s^2.