Answer:
The number of seconds required to complete 7 revolutions is 236.28 s.
Step-by-step explanation:
Given;
speed of the point on the wheel, ω = 32π/9 rad/min
number of revolutions made by the point, θ = 7 rev
The time taken for the point to make 7 revolutions is calculated as follows;
1 rev = 2π rad
[tex]time (t) = \frac{\theta }{\omega} = \theta \ \times \frac{1}{\omega} \\\\t = (7 \ rev \ \times \frac{2 \pi \ rad}{1 \ rev} ) \ \times (\frac{1}{32 \pi/9 \ \frac{rad}{\min} } )\\\\t = (7 \times 2\pi \ \ rad) \times (\frac{9}{32 \pi }\frac{\min}{rad}) \\\\t = 14 \pi \ (rad) \ \times \ \frac{9}{32 \pi}\ (\frac{\min}{rad} )\\\\t = \frac{14 \times 9}{32} \ \min\\\\t = 3.938 \ \min\\\\t = 3.938 \ (\min) \times \frac{60 \ s}{1 \ \min} \\\\t = 236.28 \ s[/tex]
Therefor, the number of seconds required to complete 7 revolutions is 236.28 s.
