Three people are standing on a horizontally rotating platform in an amusement park. one person is almost at the edge, the second one is (3/5)r from the center, and the third is (1/2)r from the center.

1-if the period of rotation of the first person is t1 = t, find in terms of tthe period of rotation of the second person.

2- if the period of rotation of the first person is t1 = t, find in terms of t the period of rotation of the third person.

3-if the speed of the first person is v1 = v find in terms of v the speed of the second person

4- if the speed of the first person is v1 = v find in terms of v the speed of the third person.

5- if the radial acceleration of the first person is a1 = a, find in terms of athe radial acceleration of the second person.

6- if the radial acceleration of the first person is a1 = a, find in terms of athe radial acceleration of the third person.

1- Period is the time for which one full rotation is completed. Regardless of their positions on the platform, periods of all three are the same. T2 = T.

2- Similarly, T3 = T.

3- The platform is making rotational motion. So, the relation between the angular velocity and the linear velocity is

For all the people, angular velocity is the same. Their linear velocities are different.

4- Similarly,

5- Radial acceleration in constant circular motion is

For the second person:

6- Similarly,

Explanation:

As a result, the period is same for every object on the rotating platform, as they all complete their revolutions at the same time. Their speed and radial acceleration is different according to their distance to the center.

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