A flywheel is rotating at 1000 rpm. If it is brought to rest in 10 seconds, what

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Question: A flywheel is rotating at 1000 rpm. If it is brought to rest in 10 seconds, what is the average angular deceleration?

Options:

Correct Answer: 20 rad/s²

Solution:

First convert rpm to rad/s: 1000 rpm = (1000 * 2π)/60 rad/s. Then use α = (ωf - ωi)/t = (0 - (1000 * 2π)/60) / 10.

A flywheel is rotating at 1000 rpm. If it is brought to rest in 10 seconds, what is the average angular deceleration?

A flywheel is rotating at 1000 rpm. If it is brought to rest in 10 seconds, what is the average angular deceleration?

Step 1: Convert the rotation speed from revolutions per minute (rpm) to radians per second (rad/s). Use the formula: rad/s = (rpm * 2π) / 60.
Step 2: Substitute 1000 rpm into the formula: (1000 * 2π) / 60 to find the initial angular velocity (ωi) in rad/s.
Step 3: Identify the final angular velocity (ωf). Since the flywheel is brought to rest, ωf = 0 rad/s.
Step 4: Use the formula for average angular deceleration (α): α = (ωf - ωi) / t, where t is the time taken to stop (10 seconds).
Step 5: Substitute the values into the formula: α = (0 - (1000 * 2π) / 60) / 10.
Step 6: Calculate the result to find the average angular deceleration.

Angular Velocity Conversion – Understanding how to convert revolutions per minute (rpm) to radians per second (rad/s) is essential for solving problems involving angular motion.
Angular Deceleration Calculation – Applying the formula for angular deceleration, which is the change in angular velocity over time, is crucial for determining how quickly the flywheel comes to rest.