which of the torques given below is required to change the angular momentum of flywheel from 15 to 150 kg m 2/s during a time interval of 5 sec? a. 25 kgm2/s2b. 27 kgm2/s2c. 29 kgm2/s2d. 31 kgm2/s2

To determine the torque required to change the angular momentum of a flywheel from 15 kg m²/s to 150 kg m²/s over a time interval of 5 seconds, we can use the relationship between torque, angular momentum, and time. The formula we need is based on the principle that torque is the rate of change of angular momentum.

Understanding the Relationship

The torque (\( \tau \)) can be calculated using the formula:

Torque (τ) = Change in Angular Momentum (ΔL) / Time (Δt)

Calculating Change in Angular Momentum

First, we need to find the change in angular momentum:

• Initial Angular Momentum (\( L_i \)) = 15 kg m²/s
• Final Angular Momentum (\( L_f \)) = 150 kg m²/s
• Change in Angular Momentum (\( ΔL \)) = \( L_f - L_i \) = 150 kg m²/s - 15 kg m²/s = 135 kg m²/s

Applying the Time Interval

Next, we will divide this change by the time interval of 5 seconds:

• Time Interval (\( Δt \)) = 5 seconds
• Torque (\( τ \)) = \( ΔL / Δt \) = 135 kg m²/s / 5 s = 27 kg m²/s²

Final Result

Thus, the torque required to change the angular momentum of the flywheel from 15 kg m²/s to 150 kg m²/s in 5 seconds is 27 kg m²/s².

Looking at the options provided, the correct answer is b. 27 kg m²/s².