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davidge
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Homework Statement
A right cylinder is at rest as in the figure below. It then starts rolling down without
Given:
Moment of inertia of the cylinder ##I = \frac{1}{2}MR^2##.
Radius of the cylinder ##R = 20 \ cm##.
Mass of the cylinder ##M = 12 \ kg##.
2. The attempt at a solution
This problem is from an exam from my undergraduate course on physics
Conservation of energy yields
Mg6Sin(30°) = MVCM2/2, where VCM is the cylinder center of mass speed and g is the gravity acceleration.
Since
I got $$\omega = \sqrt{6g} / R = 10 \sqrt{ \frac{3g}{2}} \ \bigg(\frac{ \text{rad}}{ \text{sec}} \bigg)$$
For the second part of the problem, I considered that the only acceleration is due to gravity (constant), in which case we can use the equations
V = V0 + at
D = V0t
$$0 = V_{0 \ - \ \text{vertical}} + gt \\
t = |V_{0 \ - \ \text{vertical}}| / |g| = \sqrt{6g} \ \text{Sin(30°)} / g = \frac{1}{2} \sqrt{ \frac{6}{g}} \ (\text{sec})$$
So, the horizontal distance is $$D = \sqrt{6g} \ \text{Cos(30°)} \times \frac{1}{2} \sqrt{ \frac{6}{g}} = 3 \frac{ \sqrt{3}}{2} \ (\text{meters})$$
Is this correct?
EDIT: The correct sentence is "the cylinder is rolling without slipping, instead of without friction".
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