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A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a

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Question: A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?

Options:

  1. 20 rad/s
  2. 10 rad/s
  3. 30 rad/s
  4. 0 rad/s

Correct Answer: 20 rad/s

Solution: 

Final angular velocity = initial angular velocity + (angular acceleration × time) = 10 + (2 × 5) = 20 rad/s.

A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a

Practice Questions

Q1
A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?
  1. 20 rad/s
  2. 10 rad/s
  3. 30 rad/s
  4. 0 rad/s

Questions & Step-by-Step Solutions

A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?
Correct Answer: 20 rad/s
  • Step 1: Identify the initial angular velocity. In this case, it is 10 rad/s.
  • Step 2: Identify the angular acceleration. Here, it is 2 rad/s².
  • Step 3: Identify the time duration for which the wheel accelerates. This is 5 seconds.
  • Step 4: Use the formula for final angular velocity: Final angular velocity = Initial angular velocity + (Angular acceleration × Time).
  • Step 5: Substitute the values into the formula: Final angular velocity = 10 rad/s + (2 rad/s² × 5 s).
  • Step 6: Calculate the product of angular acceleration and time: 2 rad/s² × 5 s = 10 rad/s.
  • Step 7: Add this result to the initial angular velocity: 10 rad/s + 10 rad/s = 20 rad/s.
  • Step 8: Conclude that the final angular velocity after 5 seconds is 20 rad/s.
  • Angular Velocity – The rate of rotation of an object, measured in radians per second.
  • Angular Acceleration – The rate of change of angular velocity, measured in radians per second squared.
  • Kinematic Equation for Rotational Motion – The equation used to calculate final angular velocity based on initial angular velocity, angular acceleration, and time.
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