Question

Two particles A and B move at a constant speed in circular paths at the same angular speed ω. Particle A's circle has a radius that is the length of particle B's circle. What is the ratio vA/vB of their translational speeds?

Answer 1

Answer:

2:1

Explanation:

It is given that,

Two particles A and B move at a constant speed in circular paths at the same angular speed ω.

Particle A's circle has a radius that is the length of particle B's circle.

We need to find the ratio of vA/vB of their translational speeds.

As the angular speed is same. The relation between angular and linear speed is given by :

$\omega=\dfrac{v}{r}\\\\\omega_A=\omgega_B\\\\\dfrac{v_A}{r_A}=\dfrac{v_B}{r_B}$

As $r_A=2r_B$

So,

$\dfrac{v_A}{2r_B}=\dfrac{v_B}{r_B}$

$\dfrac{v_A}{v_B}=2$

So, the ratio of their translational speeds is 2:1.