Question

The angular speed of motor wheel is increased from 1200 rpm to 3120 rpm in 16 sec. The angular acceleration of the motor wheel is

• A. 6π rad/s2
• B. 2π rad/s2
• C. 8π rad/s2
• D. 4π rad/s2

Answer 1

Answer: (D)

4π rad/s2

Answer 2

To find the angular acceleration, we can use the following formula:
Angular acceleration (α) = (Final angular velocity (ωf) - Initial angular velocity (ωi)) / Time taken (t)
Given:
Initial angular velocity (ωi) = 1200 rpm
Final angular velocity (ωf) = 3120 rpm
Time taken (t) = 16 sec
First, let's convert the angular velocities from rpm to radians per second (rad/s):
1 revolution = 2π radians
1 minute = 60 seconds
Initial angular velocity (ωi) = 1200 rpm * (2π radians/1 revolution) * (1 minute/60 seconds)
= 1200 * 2π * (1/60) rad/s
= 40π rad/s
Final angular velocity (ωf) = 3120 rpm * (2π radians/1 revolution) * (1 minute/60 seconds)
= 3120 * 2π * (1/60) rad/s
= 104π rad/s
Now, we can calculate the angular acceleration (α):
α = (ωf - ωi) / t
= (104π - 40π) / 16
= 64π / 16
= 4π rad/s2
Therefore, the angular acceleration of the motor wheel is 4π rad/s2, which corresponds to option (D).