Question

The angular velocity of a rigid body about any point of that body is same

• A. only in magnitude
• B. only in direction
• C. both in magnitude and direction necessarily
• D. both in magnitude and direction about some points but not about all points.

Answer 1

The correct option is C both in magnitude and direction necessarily

Suppose a rod is having angular velocity ${}^{\prime }{\omega }^{\prime }$ about point ${}^{\prime }{C}^{\prime }$, and the rod is moving with speed ${}^{\prime }{v}^{\prime }$ as shown below.



Let us choose two points $A$ and $B$ as shown in figure.
Velocity of $B$ w.r.t $A$
$V_{BA}=(v+\omega r_1)-(v-\omega r_2)$
$V_{BA}=\omega (r_1+r_2)$
Angular velocity of $B$ w.r.t $A$
${\omega }_{BA}=\frac{V_{BA}}{AB}$
${\omega }_{BA}=\frac{\omega (r_1+r_2)}{r_1+r_2}=\omega$