# Pulley & Top

1. Dec 1, 2004

### Cyto

i have no idea how to do these questions, and was wondering if you guys could help out:

a m1=16.6kg mass and a m2=10.6kg mass are suspended by a pulley that has a radius of R=11.1cm and a mass of M= 3.20kg... The cord has a negligible mass and causes the pullet to rotate without slipping. The pulley rotates without friction. The masses start from rest a d=2.81 m distance apart on either side of the pulley. Treating the pulley as a uniform disk, determine the speeds of the two masses as they pass each other.

&

A top has a moment of inertia of 3.70e-4 kg-m^2 and is initially at rest. A string wrapped around a peg along the axis of the top is pulled in such a manner that a constant tension of 5.17N is maintained. If the string does not slip while it is unwound from the peg, what is the angular speed of the top after 83.0cm of string has been pulled off the peg?

2. Dec 1, 2004

### prasanna

You might have done problems with involving a massless pulley.
In such type of problems, if there is just one pulley and there are two masses hanging on both sides, we took tension to be equal of both the parts of the cord.
Here it is not so.

Call $$T_1$$ to be the tension in the part holding $$m_1$$
and $$T_2$$ to be the tension in the part holding $$m_2$$

now the tensions produce torque upon the pulley.
on will be clockwise and the other will be anticlockwise.
Torque1,$$\tau_1 = rT_1$$
other one,$$\tau_2 = rT_2$$
resultant = $$\tau = r(T_{1} - T_{2})$$

but,
$$\tau = I\alpha = I\frac{a}{r}$$

Try to do it from here !!

Last edited: Dec 1, 2004