# Calculate the radius of a circle and the frequency of revolution of a body that moves uniformly in a circle

**Calculate the radius of a circle and the frequency of revolution of a body that moves uniformly in a circle at a speed of 0.6 m / s and a centripetal acceleration of 0.9 m / s**

V = 0.6 m / s.

a = 0.9 m / s2.

R -?

v -?

With a uniform movement of the body around the circle, due to a change in the direction of the body’s velocity, the body moves with centripetal acceleration a, the value of which is determined by the formula: a = V ^ 2 / R. Where V is the body’s velocity, R is the radius of the circle.

R = V ^ 2 / a.

R = (0.6 m / s) ^ 2 / 0.9 m / s2 = 0.4 m.

The frequency of rotation v is the number of revolutions of the body per unit of time. Frequency v is the reciprocal of the period of rotation T: v = 1 / T. The period T is the time of one complete revolution.

T = S / V = 2 * P * R / V.

v = V / 2 * P * R.

v = 0.6 m / s 2 * 3.14 * 0.4 m = 0.24 Hz.

Answer: the radius of the circle is R = 0.4 m, the rotation frequency is v = 0.24 Hz.