Theangular speed of a car increases from 600 rpm to 1200 rpm in 10 s .What is the angular acceleration of the car ?

Options

A. `600 rads^(-2)`
B. `60 rads^(-2)`
C. `60pi rads^(-2)`
D. `2pi rads^(-2)`

Explanation

To find the angular acceleration of the car, we can follow these steps:

### Step 1: Convert Angular Speeds from RPM to Radians per Second
The car's angular speeds are given in revolutions per minute (rpm). We need to convert these to radians per second (rad/s) using the conversion factor:

\[ \text{Angular speed in rad/s} = \text{Angular speed in rpm} \times \frac{2\pi \text{ rad}}{1 \text{ rev}} \times \frac{1 \text{ min}}{60 \text{ s}} \]

1. **Initial angular speed (\( \omega_1 \))**:
\[ \omega_1 = 600 \text{ rpm} = 600 \times \frac{2\pi}{60} = 20\pi \text{ rad/s} \]

2. **Final angular speed (\( \omega_2 \))**:
\[ \omega_2 = 1200 \text{ rpm} = 1200 \times \frac{2\pi}{60} = 40\pi \text{ rad/s} \]

### Step 2: Calculate the Change in Angular Velocity
Now, we can find the change in angular velocity (\( \Delta \omega \)):
\[ \Delta \omega = \omega_2 - \omega_1 = 40\pi - 20\pi = 20\pi \text{ rad/s} \]

### Step 3: Calculate Angular Acceleration
Angular acceleration (\( \alpha \)) is defined as the change in angular velocity divided by the time taken for that change:
\[ \alpha = \frac{\Delta \omega}{\Delta t} \]
Where \( \Delta t = 10 \text{ s} \):
\[ \alpha = \frac{20\pi}{10} = 2\pi \text{ rad/s}^2 \]

### Final Answer
The angular acceleration of the car is:
\[ \alpha = 2\pi \text{ rad/s}^2 \]