rotation about a fixed axis?

Question

A sphere of mass 20 kg and radius 2 m starts from rest and rotates with a constant
angular acceleration of 4 rad/s2 about a fixed axis through its center. After 4.8 s, what
is the kinetic energy (in kJ) of the sphere?

W = 4
M = 20
R = 2

Krot = 1/2 I W^2, I for a sphere 2/5M*R^2
Replacing I in the equation, Krot = 1/2(2/5M*R^2)W^2
The answer should be 5.9 in kJ. Where did I go wrong? :(

Answer 1

First, you need to calculate the angular velocity, omega, after the acceleration of 4 rad/sec^2 has acted on it for 4.8 seconds. So...

4 rad/sec^2 * 4.8 sec = 19.52 rad/sec

Now, you can plug this into the equation with I = 2/5MR^2...

Krot = 1/2*(2/5)*(20kg)*(2m^2)*((19.52rad/sec)^2)

= about 6.1 kJ

Answer 2

You are using the formula for rotation with constant angular velocity. The angular velocity here isn't const.

As far as I understood the notation, W=4 rad/sec2 is acceleration. But you pluged it in as if it were angular velocity.