Answer :
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
Step-by-step 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,
[tex]\omega = 5\ \frac{rev}{\min} \times \frac{2\pi \ rad}{1 \ rev} \ \times \frac{1 \min}{60 \ s} = \frac{10\pi \ rad}{60 \ s} = \frac{\pi }{6} rad/s[/tex]
After 1 second, the angular distance turned by the wheel is calculated as;
[tex]\theta = \omega t\\\\\theta = \frac{\pi \ rad} {6 \ s} \times 1 \ s\\\\\theta = \frac{\pi } {6 } \ rad\\\\in \ degrees; \theta = \frac{\pi \ rad}{6} \times \frac{180^0}{\pi \ rad} = \frac{180^0}{6} = 30^0[/tex]
Therefore, the angle subtended at the centre by the minor arc is 30⁰