Question 473: Centre of Mass and Rotational Motion

Question

One end of a straight uniform 1m long bar is
pivoted on horizontal table. It is released from
rest when it makes an angle 30º from the
horizontal (see figure). Its angular speed when
it hits the table is given as $\sqrt n $ s
-1
, where n is
an integer. The value of n is _________.
![](https://imagex.cdn.examgoal.net/7k9k2k5inx220/932791e2-6cc1-40c3-959d-22be95ac1d9f/8e295280-396e-11ea-92dd-4b9c3519996f/file-7k9k2k5inx221-169w.jpg)

Accepted Answer

By energy conservation
U
i
+ K
i
= U
f
+ K
f
$ \Rightarrow $ $mg{l \over 2}\sin 30^\circ $ + 0 = 0 + ${1 \over 2}I{\omega ^2}$
$ \Rightarrow $ $mg{1 \over 2} 	imes {1 \over 2}$ = ${1 \over 2} 	imes {{m{{\left( 1 ight)}^2}} \over 3}{\omega ^2}$
$ \Rightarrow $ ${\omega ^2} = {{3g} \over 2}$
$ \Rightarrow $ $\omega  = \sqrt {15} $
$ 	herefore $ n = 15

Centre of Mass and Rotational Motion

One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30º from the horizontal (see figure). Its angular speed when it hits the table is given as \sqrt n s -1 , where n is an integer. The value of n is _________.

Integer / Numeric Answer Type