A flywheel is rotating with an angular speed of 20 rad/s. If it experiences a torque of 5 Nm, what is the time taken to stop it?

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Q: A flywheel is rotating with an angular speed of 20 rad/s. If it experiences a torque of 5 Nm, what is the time taken to stop it?

Solution: Using τ = Iα, we find α = τ/I. Assuming I = 1 kg·m², α = 5 rad/s². Time to stop = ω/α = 20 rad/s / 5 rad/s² = 4 s.

Steps: 5

Step 1: Identify the given values. The angular speed (ω) is 20 rad/s and the torque (τ) is 5 Nm.
Step 2: Use the formula τ = Iα to relate torque (τ), moment of inertia (I), and angular acceleration (α).
Step 3: Assume the moment of inertia (I) is 1 kg·m² for simplicity.
Step 4: Calculate the angular acceleration (α) using the formula α = τ/I. Substitute τ = 5 Nm and I = 1 kg·m²: α = 5 Nm / 1 kg·m² = 5 rad/s².
Step 5: To find the time taken to stop, use the formula time = ω/α. Substitute ω = 20 rad/s and α = 5 rad/s²: time = 20 rad/s / 5 rad/s² = 4 s.