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What is the angular velocity of a wheel rotating at 300 revolutions per minute?

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Question: What is the angular velocity of a wheel rotating at 300 revolutions per minute?

Options:

  1. 10Ï€ rad/s
  2. 20Ï€ rad/s
  3. 30Ï€ rad/s
  4. 40Ï€ rad/s

Correct Answer: 20Ï€ rad/s

Solution: 

Angular velocity (ω) = 2π * (300/60) = 10π rad/s.

What is the angular velocity of a wheel rotating at 300 revolutions per minute?

Practice Questions

Q1
What is the angular velocity of a wheel rotating at 300 revolutions per minute?
  1. 10Ï€ rad/s
  2. 20Ï€ rad/s
  3. 30Ï€ rad/s
  4. 40Ï€ rad/s

Questions & Step-by-Step Solutions

What is the angular velocity of a wheel rotating at 300 revolutions per minute?
  • Step 1: Understand that angular velocity (ω) is measured in radians per second (rad/s).
  • Step 2: Know that 1 revolution is equal to 2Ï€ radians.
  • Step 3: Convert revolutions per minute (rpm) to revolutions per second (rps) by dividing by 60. So, 300 rpm becomes 300/60 = 5 rps.
  • Step 4: Multiply the number of revolutions per second (5 rps) by 2Ï€ to find the angular velocity. So, ω = 2Ï€ * 5.
  • Step 5: Calculate the result: 2Ï€ * 5 = 10Ï€ rad/s.
  • Angular Velocity – Angular velocity is the rate of change of angular displacement and is typically measured in radians per second.
  • Conversion of Units – Understanding how to convert revolutions per minute (RPM) to radians per second is crucial for solving the problem.
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