A flywheel is rotating with an angular velocity of 20 rad/s. If it experiences a

What’s inside this PDF?

Question: A flywheel is rotating with an angular velocity of 20 rad/s. If it experiences a constant torque that reduces its angular velocity to 10 rad/s in 5 seconds, what is the magnitude of the torque if the moment of inertia is 4 kg·m²?

Options:

8 N·m
4 N·m
2 N·m
10 N·m

Correct Answer: 4 N·m

Solution:

The angular deceleration α = (ω_final - ω_initial) / time = (10 - 20) / 5 = -2 rad/s². Torque τ = Iα = 4 kg·m² * (-2 rad/s²) = -8 N·m, so the magnitude is 8 N·m.

Practice Questions

Q1

A flywheel is rotating with an angular velocity of 20 rad/s. If it experiences a constant torque that reduces its angular velocity to 10 rad/s in 5 seconds, what is the magnitude of the torque if the moment of inertia is 4 kg·m²?

8 N·m
4 N·m
2 N·m
10 N·m

Questions & Step-by-Step Solutions

A flywheel is rotating with an angular velocity of 20 rad/s. If it experiences a constant torque that reduces its angular velocity to 10 rad/s in 5 seconds, what is the magnitude of the torque if the moment of inertia is 4 kg·m²?

Step 1: Identify the initial angular velocity (ω_initial) which is 20 rad/s.
Step 2: Identify the final angular velocity (ω_final) which is 10 rad/s.
Step 3: Identify the time duration (t) over which the change occurs, which is 5 seconds.
Step 4: Calculate the angular deceleration (α) using the formula: α = (ω_final - ω_initial) / time.
Step 5: Substitute the values: α = (10 - 20) / 5 = -2 rad/s².
Step 6: Identify the moment of inertia (I) which is 4 kg·m².
Step 7: Calculate the torque (τ) using the formula: τ = I * α.
Step 8: Substitute the values: τ = 4 kg·m² * (-2 rad/s²) = -8 N·m.
Step 9: The magnitude of the torque is the absolute value, which is 8 N·m.

Angular Velocity – The rate of rotation of an object, measured in radians per second.
Torque – A measure of the rotational force applied to an object, calculated as the product of moment of inertia and angular acceleration.
Moment of Inertia – A property of a body that defines its resistance to angular acceleration, dependent on mass distribution.
Angular Deceleration – The rate of decrease of angular velocity, which can be calculated from the change in angular velocity over time.

A flywheel is rotating with an angular velocity of 20 rad/s. If it experiences a

What’s inside this PDF?

A flywheel is rotating with an angular velocity of 20 rad/s. If it experiences a

Practice Questions

Questions & Step-by-Step Solutions

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