# With what translation should the carousel with a radius of 6.4 m rotate in order for the centripetal

With what translation should the carousel with a radius of 6.4 m rotate in order for the centripetal acceleration of a person on the carousel to be equal to 10 m / s.

R = 6.4 m.

a = 10 m / s2.

T -?

The period of rotation T is the time of one complete revolution. The period T is expressed by the formula: T = L / V, where L is the circumference that the carousel goes through in 1 revolution, V is the speed of rotation of the carousel.

The length of the circle L, which the carousel passes, is expressed by the formula: L = 2 * P * R.

The centripetal acceleration a is expressed by the formula: a = V2 / R.

V = √ (a * R).

T = 2 * P * R / √ (a * R).

T = 2 * 3.14 * 6.4 m / √ (10 m / s2 * 6.4 m) = 5 s.

Answer: the period of rotation of the carousel is T = 5 s.

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