A flywheel has a moment of inertia I and is rotating with an angular velocity ω.
Practice Questions
Q1
A flywheel has a moment of inertia I and is rotating with an angular velocity ω. If a torque τ is applied for time t, what is the final angular velocity?
ω + (τ/I)t
ω - (τ/I)t
ω + (I/τ)t
ω - (I/τ)t
Questions & Step-by-Step Solutions
A flywheel has a moment of inertia I and is rotating with an angular velocity ω. If a torque τ is applied for time t, what is the final angular velocity?
Step 1: Identify the initial angular velocity (ω) of the flywheel.
Step 2: Determine the moment of inertia (I) of the flywheel.
Step 3: Apply the torque (τ) to the flywheel for a certain time (t).
Step 4: Calculate the angular acceleration (α) using the formula α = τ/I.
Step 5: Use the formula for final angular velocity: ω_f = ω + αt.
Step 6: Substitute α from Step 4 into the final angular velocity formula: ω_f = ω + (τ/I)t.
Step 7: This gives you the final angular velocity (ω_f) after applying the torque.
Moment of Inertia – The resistance of a body to change its rotational motion, dependent on mass distribution.
Torque – A measure of the force that can cause an object to rotate about an axis.
Angular Acceleration – The rate of change of angular velocity, calculated as α = τ/I.
Kinematic Equation for Rotational Motion – The equation ω_f = ω + αt relates initial angular velocity, angular acceleration, and time.
