What is the magnitude and direction of the force acting on the ball?

Question

A small ball of 30 grams makes a smooth circular motion. The radius of the circular orbit is 25 centimeters to make a complete circle

time required 3 seconds. What is the magnitude and direction of the force acting on the ball?

Answer 1

F = ma so we just need to find the acceleration.

For uniform circular motion there is an acceleration pointed inwards toward the center of the circle of revolution and that acceleration can be thought of as either v²/r (v is the tangential velocity) or as ω²r (ω is the angular velocity). Since in this case we are given elements to calculate the angular velocity, we can use ω²r.

ω is radians/sec = 2π/(3 sec) = (2/3)π radians/sec and r = 30 cm = 0.3 m. So:

a = ω²r = ((2/3)π)²(0.3)

a = 1.3159 m/s²

m = 30 g = 0.03 kg so:

F = ma = (0.03)(1.3159) = 0.0395 N or, rounding to 1 sig fig, F = 0.04 N with the direction again pointing inwards toward the center of the circle of revolution