Question 653: Centre of Mass and Rotational Motion

Question

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s$$-$$2 is

Accepted Answer

Here $$\alpha $$ = 2 revolutions/s
2
= 4$$\pi $$ rad/s
2
(given)
$${I_{cylinder}} = {1 \over 2}M{R^2} = {1 \over 2}\left( {50} ight){\left( {0.5} ight)^2} = {{25} \over 4}{m{Kg - }}{{m{m}}^{m{2}}}$$
As $$	au  = I\alpha $$ so $$TR = I\alpha $$
$$ \Rightarrow T = {{I\alpha } \over R} = {{\left( {{{25} \over 4}} ight)\left( {4\pi } ight)} \over {0.5}}N$$
= 50 $$\pi $$N = 157 N

Answer

25 N

Answer

50 N

Answer

78.5 N

Answer

157 N

Centre of Mass and Rotational Motion

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s$-$2 is

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