Question 632: Centre of Mass and Rotational Motion

Question

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2$$\pi $$ revolutions is :

Accepted Answer

Acccording to work energy theorem,
W = $${1 \over 2}\left( {\omega _f^2 - \omega _i^2} ight)$$
Given that,
$$	heta $$ = 2$$\pi $$ revolution/minute
$$	heta $$ = 2$$\pi $$ $$ 	imes $$ 2$$\pi $$ = 4$$\pi $$
2
rad
$${\omega _i} = 3 	imes {{2\pi } \over {60}}$$ rad/s
$${\omega _f} = 0$$ rad/s
By putting the value of $${\omega _f}$$ and $${\omega _i}$$, we get
- $$	au $$$$	heta $$ = $${1 \over 2} 	imes {1 \over 2}m{r^2}\left( {0 - \omega _i^2} ight)$$
$$ \Rightarrow $$ $$	au $$ = $$ - {{{1 \over 2} 	imes {1 \over 2} 	imes 2 	imes \left( {4 	imes {{10}^{ - 2}}} ight) 	imes {{\left( { - 3 	imes {{2\pi } \over {60}}} ight)}^2}} \over {4{\pi ^2}}}$$
= 2 $$ 	imes $$ 10
-6
Nm

Answer

2 × 10
–3
N m

Answer

2 × 10
–6
N m

Answer

2 × 10
6
N m

Answer

12 × 10
–4
N m

Centre of Mass and Rotational Motion

A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm. The torque required to stop after 2$\pi $ revolutions is :

Choose the correct answer: