Question

A wheel of radius 10 cm is turning at a rate of 5 revolutions per minute.

Calculate : the angle subtended at the centre by the minor arc.

Answer 1

Complete question:

A wheel of radius 10 cm is turning at a rate of 5 revolutions per minute.

Calculate the angle subtended at the centre by the minor arc after 1 second.

Answer:

the angle subtended at the centre by the minor arc is 30⁰

Explanation:

Given;

radius of the wheel, r = 10 cm = 0.1 m

angular speed of the when, ω = 5 rev/min

duration of the motion, t = 1 second

Determine the angular speed in radian per second,

`\omega = 5\ (rev)/(\min) * (2\pi \ rad)/(1 \ rev) \ * (1 \min)/(60 \ s) = (10\pi \ rad)/(60 \ s) = (\pi )/(6) rad/s`

After 1 second, the angular distance turned by the wheel is calculated as;

`\theta = \omega t\\\\\theta = \frac{\pi \ rad} {6 \ s} * 1 \ s\\\\\theta = \frac{\pi } {6 } \ rad\\\\in \ degrees; \theta = (\pi \ rad)/(6) * (180^0)/(\pi \ rad) = (180^0)/(6) = 30^0`

Therefore, the angle subtended at the centre by the minor arc is 30⁰