Question 736: Centre of Mass and Rotational Motion

Question

A cylinder of mass m and radius R rolls 
down on an inclined plane of inclination $$	heta$$. 
Calculate the linear acceleration of axis of 
cylinder.

Accepted Answer

Acceleration of a body rolling down the inclined plane
$$a = {{g\sin 	heta } \over {1 + {I \over {m{R^2}}}}}$$
For cylinder, $$\quad \mathrm{I}=\frac{1}{2} m \mathrm{R}^{2}$$
$$a = {{g\sin 	heta } \over {1 + {{{1 \over 2}m{R^2}} \over {m{R^2}}}}} = {{g\sin 	heta } \over {1 + {1 \over 2}}}$$
$$a = {{g\sin 	heta } \over {{3 \over 2}}}$$
$$a = {2 \over 2}g\sin 	heta $$

Answer

$$a=\frac{2}{3} g \sin 	heta$$

Answer

$$a= g \sin 	heta$$

Answer

$$a=\frac{5}{3} g \sin 	heta$$

Answer

$$a=\frac{7}{3} g \sin 	heta$$

Centre of Mass and Rotational Motion

A cylinder of mass m and radius R rolls down on an inclined plane of inclination $\theta$. Calculate the linear acceleration of axis of cylinder.

Choose the correct answer: