A wheel rotates with a constant angular velocity of 600 rpm. What is the angle through which the wheel rotates in 1s?

Options

A. `5pi` rad
B. `20 pi`rad
C. `15 pi` rad
D. `10pi` rad

Answer

To solve the problem of finding the angle through which a wheel rotates in 1 second when it has a constant angular velocity of 600 rpm, we can follow these steps:

### Step 1: Convert RPM to Radians per Second
First, we need to convert the angular velocity from revolutions per minute (rpm) to radians per second. The formula to convert rpm to radians per second is:

\[ \omega = 2\pi n \times \frac{1}{60} \]

where \( n \) is the angular velocity in rpm.

Given:
- \( n = 600 \, \text{rpm} \)

Substituting the value of \( n \):

\[ \omega = 2\pi \times 600 \times \frac{1}{60} \]

### Step 2: Calculate the Angular Velocity
Now, we can simplify the expression:

\[ \omega = 2\pi \times 600 \times \frac{1}{60} = 2\pi \times 10 = 20\pi \, \text{radians per second} \]

### Step 3: Calculate the Angle Rotated in 1 Second
The angle rotated in a given time can be calculated using the formula:

\[ \Delta \theta = \omega \times t \]

where \( t \) is the time in seconds. For our case, \( t = 1 \, \text{s} \).

Substituting the values:

\[ \Delta \theta = 20\pi \times 1 = 20\pi \, \text{radians} \]

### Step 4: Conclusion
Thus, the angle through which the wheel rotates in 1 second is:

\[ \Delta \theta = 20\pi \, \text{radians} \]

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