Question

A small metal object is tied to the end of a string and whirled round a circular path of radius 30cm. The object makes 20 oscillations in 5 seconds. Calculate: the angular and linear speeds of the object

Answer 1

(i) The angular speed of the small metal object is 25.133 rad/s

(ii) The linear speed of the small metal object is 7.54 m/s.

Step-by-step explanation:

Given;

radius of the circular path, r = 30 cm = 0.3 m

number of revolutions, n = 20

time of motion, t = 5 s

(i) The angular speed of the small metal object is calculated as;

`\omega = (20 \ rev)/(5 \ s) * (2 \pi \ rad)/(1 \ rev) = (40\pi \ rad)/(5 \ s) = 8\pi \ rad/s = 25.133 \ rad/s`

(ii) The linear speed of the small metal object is calculated as;

`v = \omega r\\\\v = 25.133 \ rad/s \ * \ 0.3 \ m\\\\v = 7.54 \ m/s`