# Rotational Dynamics

1. Nov 13, 2004

### Electro

Hello,
I have a problem dealing with torques and acceleration. I am sure I solved it right but when submitting the answers, I get the response "Incorrect"

The problem:

A wheel of radius 2 m, mass 53 kg, and moment of inertia (3/4) (53 kg) (2m)^2 about the center of mass is mounted on a frictionless horizontal axle.
(g = 9.8). A light cord wrapped around the wheel supports an object of mass 106 kg. The weight is released from rest at the level of A and falls a distance h, past level B (AB=28 m). a) Find the velocity as it passes B b) Determine the tension of the string.

I set up everything.

Torque = I* alpha = T*R since alpha = a/R and we know I, conclusion is T=42*a

Then: T=m(g - a): putting T from above, I got a=7.0189189 m/s^2
To find V as the mass passes point B: Vf^2 = 2*a*28m ---> and v at B = 19.83 m/s. This was OK

For b) I used T=m(g-a), since I know a = 7.0189189m/s^2 , I substituted it at the equation and I got T= 294.79 N but this is not the right answer.

Maybe I can use I*alpha = T*R and from that get T because everything is known, but I am not sure. Any suggestions?

2. Nov 13, 2004

### Electro

Can anyone help?

3. Nov 13, 2004

### CartoonKid

For part a)
F=mg
Torque=mgr
mgr=I(alpha)
28=r(theta)
Wf^2=Wi^2+2(alpha)(theta)
Vf=r(Wf)

For part b)
a=R(alpha)
T=m(g-a)

Do these things help?