Answer:
The wheel will go through 1146 revolutions in 5 minutes.
Explanation:
We can the formula:
[tex]\boxed{\omega = \frac{2 \pi}{T}}[/tex]
where
ω ⇒ angular speed (24 rad/s),
T ⇒ time period (? s),
and solve for T to find the time it takes for the wheel to complete one revolution.
⇒ [tex]24 = \frac{2 \pi}{T}[/tex]
⇒ [tex]T = \bf \frac{2 \pi}{24}[/tex] s
This means it takes [tex]\bf \frac{2 \pi}{24}[/tex] seconds for the wheel to complete one revolution.
Now, using the unitary method,
In [tex]\frac{2 \pi}{24}[/tex] seconds ⇒ 1 revolution completed
In 1 second ⇒ 1 ÷ [tex]\frac{2 \pi}{24}[/tex] = [tex]\frac{24}{2 \pi}[/tex] revolutions completed
In (5 × 60 = ) 300s ⇒ [tex]\frac{24}{2 \pi}[/tex] × 300 = 1145.9
≅ 1146 revolutions completed
