# Angular Acceleration of a grinding wheel

1. Nov 25, 2008

### spirited

1. The problem statement, all variables and given/known data
A vertical grinding wheel is a uniform disk of mass 62 kg and radius 45 cm. It has a handle of radius 69 cm of negligible mass. A 25-kg load is attached to the handle when it is in the horizontal position.
(a) Neglecting friction, find the initial angular acceleration of the wheel in rad/s^2.
(b) Find the maximum angular velocity of the wheel in rad/s.

2. Relevant equations
I = 1/2MR^2 + mr^2
t = mgr for torque
a = t/I for angular acceleration
mgr = 1/2Iw^2
3. The attempt at a solution

a) Neglecting friction, find the initial angular acceleration of the wheel.
I found I which is 18.18 kg m^2 using the above equation.
I then gound T(t) which is 169.23 Nm
a = t/I = 9.31 rad/s^2

(b) Find the maximum angular velocity of the wheel.
I used mgr = 0.5Iw^2 and got w = 3.32 rad/s

***What am I doing wrong?? I know both are wrong answers. I think I am doing something wrong for part a. Please help!!
Thanks

2. Nov 25, 2008

### LowlyPion

Welcome to PF.

I think for a) your method is OK. I calculate 9.2 m/s2
with I = 18.38 but let's not quibble too much over that.

For b) though I think you are overlooking that the 25 kg weight has dropped .69 m and not the r of .45.

3. Nov 25, 2008

### spirited

I understand it now....Thanks.