The body moves in a circle with a radius of 3 m and makes 2 complete revolutions in 10 seconds. Find acceleration.

Given:

r = 3 meters – the radius of the circle along which the body moves;

pi = 3.14 – geometric constant (Pythagoras number);

n = 2 – the number of complete revolutions made by the body during the time interval t;

t = 10 seconds – time span.

It is required to determine a (m / s2) – the centripetal acceleration of the body.

Let’s find the time for which the body makes one revolution around the circle:

t1 = t / n = 10/2 = 5 seconds.

Let’s find the length of the circle along which the body moves:

c = 2 * pi * r = 2 * 3.14 * 3 = 6 * 3.14 = 18.84 meters.

Then the speed of the body is equal to:

v = c / t1 = 18.84 / 5 = 3.8 m / s (result rounded to one decimal place).

The acceleration of the body will be equal to:

a = v2 / r = 3.82 / 3 = 14.44 / 3 = 4.8 m / s2.

Answer: the centripetal acceleration of the body is 4.8 m / s2.