Question

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

Answer 1

The wheel will go through 1146 revolutions in 5 minutes.

Step-by-step explanation:

We can the formula:

`\boxed{\omega = (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 = (2 \pi)/(T)`

⇒
`T = \bf (2 \pi)/(24)` s

This means it takes
`\bf (2 \pi)/(24)` seconds for the wheel to complete one revolution.

Now, using the unitary method,

In
`(2 \pi)/(24)` seconds ⇒ 1 revolution completed

In 1 second ⇒ 1 ÷
`(2 \pi)/(24)` =
`(24)/(2 \pi)` revolutions completed

In (5 × 60 = ) 300s ⇒
`(24)/(2 \pi)` × 300 = 1145.9

≅ 1146 revolutions completed