Question 344: Centre of Mass and Rotational Motion

Question

A cubical block of side 30 cm is moving with velocity 2 ms−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular
velocity (in rad/s) of the block immediately after it hits the bump, is :

Accepted Answer

Before hitting point 0,
angular moment = mv $$ 	imes $$ $${a \over 2}$$
After hitting point 0,
Angular momentum  = $${m I}\omega $$
$$ 	herefore $$    $${m I}\omega $$ = $${{mva} \over 2}$$
$$ \Rightarrow $$   $$\omega $$ = $${{mva} \over {2{m I}}}$$
$${m I}$$ = moment of inertia about edge,
=   $${{m{a^2}} \over 6} + m{\left( {{a \over {\sqrt 2 }}} ight)^2}$$
=   $${{m{a^2}} \over 6} + {{m{a^2}} \over 2}$$
=   $${{2m{a^2}} \over 3}$$
$$ 	herefore $$   $$\omega $$ = $${{mva} \over {2 	imes {{2m{a^2}} \over 3}}}$$ = $${{3v} \over {4a}}$$ = $${{3 	imes 2} \over {4 	imes 0.3}}$$ = 5 rad/s

Answer

5.0

Answer

6.7

Answer

9.4

Answer

13.3

Centre of Mass and Rotational Motion

A cubical block of side 30 cm is moving with velocity 2 ms−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

Choose the correct answer: