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A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2

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Question: A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2 rad/s², what will be its angular velocity after 5 seconds? (2023)

Options:

  1. 20 rad/s
  2. 10 rad/s
  3. 15 rad/s
  4. 25 rad/s

Correct Answer: 20 rad/s

Exam Year: 2023

Solution: 

Using the formula ω = ω₀ + αt, we have ω = 10 rad/s + (2 rad/s²)(5 s) = 20 rad/s.

A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2

Practice Questions

Q1
A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2 rad/s², what will be its angular velocity after 5 seconds? (2023)
  1. 20 rad/s
  2. 10 rad/s
  3. 15 rad/s
  4. 25 rad/s

Questions & Step-by-Step Solutions

A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at 2 rad/s², what will be its angular velocity after 5 seconds? (2023)
  • Step 1: Identify the initial angular velocity (ω₀). In this case, it is 10 rad/s.
  • Step 2: Identify the angular acceleration (α). Here, it is 2 rad/s².
  • Step 3: Identify the time (t) for which the wheel accelerates. In this case, it is 5 seconds.
  • Step 4: Use the formula for angular velocity: ω = ω₀ + αt.
  • Step 5: Substitute the values into the formula: ω = 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 the result to the initial angular velocity: ω = 10 rad/s + 10 rad/s = 20 rad/s.
  • Angular Velocity – Angular velocity is the rate of change of angular displacement and is measured in radians per second.
  • Angular Acceleration – Angular acceleration is the rate of change of angular velocity and is measured in radians per second squared.
  • Kinematic Equation for Rotational Motion – The equation ω = ω₀ + αt relates initial angular velocity (ω₀), angular acceleration (α), and time (t) to find final angular velocity (ω).
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