(adsbygoogle = window.adsbygoogle || []).push({}); 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 [tex]\alpha = 30[/tex]° 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

[tex] I =\frac{2}{3}MR^{2} [/tex]

[tex] K = \frac{1}{2}Mv^{2} + \frac{1}{2}I\omega^{2} [/tex]

[tex] \omega = \frac{v}{r} [/tex]

3. The attempt at a solution

(a)

[tex] mgh = \frac{1}{2}Mv^{2} + \frac{1}{2}I\omega^{2} [/tex]

[tex] gh = \frac{1}{2}v^{2} + \frac{1}{3}R^{2}\omega^{2} [/tex]

[tex] gh = \frac{1}{2}v^{2} + \frac{1}{3}R^{2}\frac{v^{2}}{R^{2}} [/tex]

[tex] gh = v^{2}(\frac{1}{2}+\frac{1}{3})[/tex]

[tex] v = \sqrt{\frac{6gh}{5}} [/tex]

(b)

[tex] \sum F_{x} = ma = mgsin(\alpha)[/tex]

[tex]a = gsin(\alpha)[/tex]

(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

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# Homework Help: Rotation of rigid bodies

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