Question

A wheel spins at a constant angular speed of 24rad/s.How many revolutions will the dosk go through in 5minutes?​

Answer 1

Answer:

The wheel will go through 1146 revolutions in 5 minutes.

Explanation:

We can the formula:

$\boxed{\omega = \frac{2 \pi}{T}}$

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.

⇒  $24 = \frac{2 \pi}{T}$

⇒  $T = \bf \frac{2 \pi}{24}$  s

This means it takes $\bf \frac{2 \pi}{24}$ seconds for the wheel to complete one revolution.

Now, using the unitary method,

In $\frac{2 \pi}{24}$ seconds          ⇒    1 revolution completed

In 1 second              ⇒    1 ÷ $\frac{2 \pi}{24}$   =  $\frac{24}{2 \pi}$  revolutions completed

In (5 × 60 = ) 300s  ⇒     $\frac{24}{2 \pi}$   ×  300   = 1145.9

                                                            ≅ 1146 revolutions completed