Calculate Total Energy: Solve Homework Statement

[Neon32]

Homework Statement

Homework Equations

Total energy = Translational kinetic energy + Rotational kinetic energy
Total energy= 1/2 m V² + 1/2 I W²

The Attempt at a Solution

W= v/r = 3.20/0.100 = 32 rad/sec
Total energy= 1/2 m V²+ 1/2 I W[²
Total energy = 1/2 (8)(3.20)² + 1/2 (1.60x10^-2) (32)²=49.152 Joule

I found a different answer in solution. Why did he find the moment of inerta? it was already given in the problem + why didn't he square the angular velocity? Please tell me why he did that and if my answer or his answer is correct.

 

[gneill]

Your method and result are correct. His is not.

The problem did not say that the bowling ball is a sphere of uniform density: the fact that the problem supplied the moment of inertia is evidence of this. So his assumption that it is a uniform sphere was flawed and his calculation of the moment of inertia was not only unnecessary but incorrect.

That he failed to square the angular velocity is also an error.

 

[Neon32]

Your method and result are correct. His is not.

The problem did not say that the bowling ball is a sphere of uniform density: the fact that the problem supplied the moment of inertia is evidence of this. So his assumption that it is a uniform sphere was flawed and his calculation of the moment of inertia was not only unnecessary but incorrect.

That he failed to square the angular velocity is also an error.

Alright. thanks for your help :).