Rotation Ques 5
- Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?
(2012)
(a) It is $\sqrt{2} \omega$ for both the cases
(b) It is $\omega$ for case (a); and $\frac{\omega}{\sqrt{2}}$ for case (b)
(c) It is $\omega$ for case (a); and $\sqrt{2} \omega$ for case (b)
(d) It is $\omega$ for both the cases
Show Answer
Answer:
Correct Answer: 5.( d )
Solution:
- (i) Every particle of the disc is rotating in a horizontal circle.
(ii) Actual velocity of any particle is horizontal.
(iii) Magnitude of velocity of any particle is $ v=r \omega $
where, $r$ is the perpendicular distance of that particle from actual axis of rotation ( $Z$-axis).
(iv) When it is broken into two parts then actual velocity of any particle is resultant of two velocities $ v_1=r_1 \omega_1 \text { and } v_2=r_2 \omega_2 $
Here,
$r_1=$ perpendicular distance of centre of mass from $Z$-axis.
$\omega_1=$ angular speed of rotation of centre of mass from $Z$-axis.
$r_2=$ distance of particle from centre of mass and $\omega_2=$ angular speed of rotation of the disc about the axis passing through centre of mass.
(v) Net $v$ will be horizontal, if $v_1$ and $v_2$ both are horizontal. Further, $v_1$ is already horizontal, because centre of mass is rotating about a vertical $Z$-axis. To make $v_2$ also horizontal, second axis should also be vertical.
BETA
