A uniform solid disk has a radius of R = 0.45 m and mass of M = 4.35 kg and is free to rotate about a fixed axis through its center of mass as shown below. It is initially at rest, and at t = 0 a constant torque is applied such that the disk starts to turn with angular acceleration a = 8*pi rad/s2.

How many revolutions has the disk made at t = 10 seconds?

What is the kinetic energy in the disk at t = 10 seconds

Question

A uniform solid disk has a radius of R = 0.45 m and mass of M = 4.35 kg and is free to rotate about a fixed axis through its center of mass as shown below. It is initially at rest, and at t = 0 a constant torque is applied such that the disk starts to turn with angular acceleration a = 8*pi rad/s2.


How many revolutions has the disk made at t = 10 seconds?

What is the kinetic energy in the disk at t = 10 seconds

anonymous · Answer

The disk has made 200 revolutions at t = 10 because 
d = 1/2 * a * t^2
d = (1/2) * (8 * pi) * 100
d = 400*pi
So then we get revolutions by dividing by 2*pi

For part b the kinetic energy of an object due to rotation is given by Ke = (1/2) * I * w^2 where I is given by (1/2)*M*r^2
So I = (1/2) * 4.35 * .45^2
I = 0.4404375

Omega (rotational velocity) can be found by using omega = alpha * t
omega = 80 * pi

Therefore kinectic energy at time 10 is 
Ke = (1/2) * I * w^2 
Ke = (1/2) * .44 * (80 * pi)^2 
Ke = 13896.403 Joules

anonymous · Answer

Thank you so much! I'm studying for my Physics final! lol