Question 633: Centre of Mass and Rotational Motion

Question

Two particles A and B are moving in uniform circular motion in concentric circles of radii r
A
and r
B
with speed v
A
and v
B
respecitively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

Accepted Answer

Since, the time period for both the particle in same
So, T
A
= T
B
= T
Angular velocity for A, ($${\omega _A}$$) = $${{2\pi } \over {{T_A}}}$$
Angular velocity for B, ($${\omega _B}$$) = $${{2\pi } \over {{T_B}}}$$
Now, the required ratio is
$${{{\omega _A}} \over {{\omega _B}}} = {{{T_B}} \over {{T_A}}} = {T \over T} = 1$$

Answer

v
A
: v
B

Answer

1 : 1

Answer

r
B
: r
A

Answer

r
A
: r
B

Centre of Mass and Rotational Motion

Two particles A and B are moving in uniform circular motion in concentric circles of radii r A and r B with speed v A and v B respecitively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

Choose the correct answer: