Compare the speeds of movement of two bodies that move with the same centripetal accelerations

Compare the speeds of movement of two bodies that move with the same centripetal accelerations in circles with radii R1 = R and R2 = 4R

Given:

R1 = R is the radius of the circle along which the first body moves;

R2 = 4 * R – radius of the circle along which the second body moves;

a1 = a2 = a – the centripetal accelerations of the two bodies are the same.

It is required to determine v2 / v1 – to compare the velocities with which the bodies are moving.

The linear velocity with which the first body moves will be equal to:

v1 = (a1 * R1) ^ 0.5 = (a * R) ^ 0.5.

The linear speed with which the second body is moving will be equal to:

v2 = (a2 * R2) ^ 0.5 = (a * 4 * R) ^ 0.5 = 2 * (a * R) ^ 0.5.

Then:

v2 / v1 = (2 * (a * R) ^ 0.5) / ((a * R) ^ 0.5) = 2, or v2 = 2 * v1.

Answer: the linear speed of the second body (moving along a circle of larger diameter) is 2 times greater than the speed of the first body.