Three people are standing on a horizontally rotating platform in an amusement pa

Question

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 T the 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.

Explanation / Answer

1) T

2) T

3) T

4) v1 = v = Rw

v2 = r2w

r2 = (3/5)*R

v2 = (3/5)*R*w = 3/5*v <----answer

5) v3 = r3w

r3 = (1/2)*R

v3 = (1/2)*R*w = (1/2)*v <----answer

6)

a1 = R*w^2 = a

a2 = r2*w^2

r2 = (3/5)*R

a2 = (3/5)*a <--answer

7)
a1 = R*w^2 = a

a3 = r3*w^2

r3 = (1/2)*R

a3 = (1/2)*a    <--answer

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