# Rotation of rigid bodies

1. Nov 30, 2008

### Amlung

1. The problem statement, all variables and given/known data

A hollow cylindrical shell with mass M = 100 g and radius R = 5 cm rolls without
slipping down an inclined plane making an angle $$\alpha = 30$$° with the horizontal.

(a) If the initial speed of the shell is zero, what will be the speed of its center of

(c) Calculate the linear acceleration of the center of mass of the shell. How long
does it take the shell to roll 1:5 meters along the plane with zero initial velocity?

(d) If the shell is replaced with a solid cylinder what will be the answer to the
previous question?

2. Relevant equations

$$I =\frac{2}{3}MR^{2}$$

$$K = \frac{1}{2}Mv^{2} + \frac{1}{2}I\omega^{2}$$

$$\omega = \frac{v}{r}$$

3. The attempt at a solution

(a)

$$mgh = \frac{1}{2}Mv^{2} + \frac{1}{2}I\omega^{2}$$

$$gh = \frac{1}{2}v^{2} + \frac{1}{3}R^{2}\omega^{2}$$

$$gh = \frac{1}{2}v^{2} + \frac{1}{3}R^{2}\frac{v^{2}}{R^{2}}$$

$$gh = v^{2}(\frac{1}{2}+\frac{1}{3})$$

$$v = \sqrt{\frac{6gh}{5}}$$

(b)

$$\sum F_{x} = ma = mgsin(\alpha)$$

$$a = gsin(\alpha)$$

(d)

According to my equation it shouldn't change anything...

I don't think b/c are correct though

Thanks for any help.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 30, 2008

### glueball8

http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/embed24.htm [Broken]

Last edited by a moderator: May 3, 2017
3. Nov 30, 2008

### Staff: Mentor

That's not the rotational inertia of a thin cylindrical shell.

Correct the moment of inertia and redo.

Gravity is not the only force acting parallel to the incline. What about friction?

But in part a you found that the speed does depend on the moment of inertia. Which means that you made a mistake in your thinking somewhere.

4. Nov 30, 2008

### Amlung

totally forgot about friction thx xD
and wrong moment of inertia...

thx ^^