What is the angular velocity of a wheel that makes 10 revolutions in 5 seconds?

What is the angular velocity of a wheel that makes 10 revolutions in 5 seconds?

Correct Answer: 4π rad/s

Step 1: Understand that one complete revolution of a wheel is equal to 2π radians.
Step 2: Calculate the total angle in radians for 10 revolutions. This is done by multiplying the number of revolutions (10) by the radians per revolution (2π). So, 10 * 2π = 20π radians.
Step 3: Identify the time taken for these revolutions, which is given as 5 seconds.
Step 4: Use the formula for angular velocity, which is ω = θ/t, where θ is the total angle in radians and t is the time in seconds.
Step 5: Substitute the values into the formula: ω = (20π radians) / (5 seconds).
Step 6: Simplify the calculation: 20π / 5 = 4π radians per second.

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