Rotation Ques 6
- Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?
(2012)
(a) It is vertical for both the cases (a) and (b)
(b) It is vertical for case (a); and is at $45^{\circ}$ to the $x$ - $z$ plane and lies in the plane of the disc for case (b)
(c) It is horizontal for case (a); and is at $45^{\circ}$ to the $x$-z plane and is normal to the plane of the disc for case (b)
(d) It is vertical for case (a); and is at $45^{\circ}$ to the $x-z$ plane and is normal to the plane of the disc for case (b)
Show Answer
Answer:
Correct Answer: 6.( a )
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
