Question

A student connects an object with mass m to a rope with a length r and then rotates the rope around her head parallel to the ground. the object takes 0.5 seconds to complete one rotation.
mass= 50 kg. length of the rope = 1.2 m
what is the objects speed of rotation?
what is the objects centripetal acceleration?
what tension force is required to maintain this motion?​

Answer 1

The object takes 0.5 seconds to complete one rotation, so its rotational speed is 1/0.5 rot/s = 2 rot/s.

Convert this to linear speed; for each rotation, the object travels a distance equal to the circumference of its path, or 2π (1.2 m) = 2.4π m ≈ 7.5 m, so that

2 rot/s = (2 rot/s) • (2.4π m/rot) = 4.8π m/s ≈ 15 m/s

thus giving it a centripetal acceleration of

a = (4.8π m/s)² / (1.2 m) ≈ 190 m/s².

Then the tension in the rope is

T = (50 kg) a ≈ 9500 N.