The wheel of a car is rotating at the rate of 1200 revolutions per minute. On pressing the accelerator for 10 sec it starts rotating at 4500 revolutions per minute. The angular acceleration of the wheel is

The correct option is 1980 degrees/sec².

To find the angular acceleration of the wheel, we can use the fundamental relation between angular acceleration, initial angular velocity, final angular velocity, and time.

Step 1: Convert the initial and final angular speeds from revolutions per minute (rpm) to degrees per second.
Recall that one full revolution is equal to 360 degrees, and one minute is equal to 60 seconds.

The initial angular speed is:
$N_1=1200\text{rpm}$

Converting this to degrees per second:
${\omega }_1=\frac{1200}{60}\times 360=20\times 360=7200\text{degrees/sec}$

The final angular speed is:
$N_2=4500\text{rpm}$

Converting this to degrees per second:
${\omega }_2=\frac{4500}{60}\times 360=75\times 360=27000\text{degrees/sec}$

Step 2: Calculate the angular acceleration.
The formula for angular acceleration ($\alpha$) is given by the change in angular velocity divided by the time interval ($t$):

$\alpha =\frac{{\omega }_2-{\omega }_1}{t}$

Given that the acceleration time interval $t=10\text{seconds}$, we substitute the values into the equation:

$\alpha =\frac{27000-7200}{10}$

$\alpha =\frac{19800}{10}=1980\text{degrees/sec}{\text{²}}^{}$

Thus, the angular acceleration of the wheel is 1980 degrees/sec².