The angular speed of a flywheel rotating at 90 r.p.m . Is

Options

A. `pi ` rad/s
B. `2pi` rad/s
C. `4 pi ` rad/s
D. `3pi ` rad/s

Explanation

To find the angular speed of a flywheel rotating at 90 revolutions per minute (r.p.m), we can follow these steps:

### Step 1: Convert revolutions per minute to revolutions per second
To convert from revolutions per minute (r.p.m) to revolutions per second (r.p.s), we divide by 60 (since there are 60 seconds in a minute).

\[ \text{Revolutions per second} = \frac{90 \text{ r.p.m}}{60} = 1.5 \text{ r.p.s} \]

### Step 2: Convert revolutions per second to radians per second
We know that one complete revolution is equal to \(2\pi\) radians. Therefore, to convert revolutions per second to radians per second, we multiply by \(2\pi\).

\[ \text{Angular speed} (\omega) = 1.5 \text{ r.p.s} \times 2\pi \text{ radians/revolution} \]

\[ \omega = 3\pi \text{ radians/second} \]

### Final Answer
The angular speed of the flywheel is \(3\pi\) radians per second.

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