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A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of in

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Question: A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of inertia of the flywheel is 2 kg·m², what is its rotational kinetic energy? (2020)

Options:

  1. 100 J
  2. 50 J
  3. 20 J
  4. 10 J

Correct Answer: 50 J

Exam Year: 2020

Solution: 

Rotational kinetic energy K.E. = (1/2)Iω² = (1/2)(2)(10)² = 100 J.

A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of in

Practice Questions

Q1
A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of inertia of the flywheel is 2 kg·m², what is its rotational kinetic energy? (2020)
  1. 100 J
  2. 50 J
  3. 20 J
  4. 10 J

Questions & Step-by-Step Solutions

A flywheel is rotating with an angular velocity of 10 rad/s. If the moment of inertia of the flywheel is 2 kg·m², what is its rotational kinetic energy? (2020)
  • Step 1: Identify the formula for rotational kinetic energy, which is K.E. = (1/2)Iω².
  • Step 2: Identify the values given in the problem: moment of inertia (I) = 2 kg·m² and angular velocity (ω) = 10 rad/s.
  • Step 3: Substitute the values into the formula: K.E. = (1/2)(2 kg·m²)(10 rad/s)².
  • Step 4: Calculate (10 rad/s)², which is 100 rad²/s².
  • Step 5: Multiply 2 kg·m² by 100 rad²/s² to get 200 kg·m²·rad²/s².
  • Step 6: Now, multiply by (1/2): (1/2)(200 kg·m²·rad²/s²) = 100 J.
  • Step 7: Conclude that the rotational kinetic energy of the flywheel is 100 Joules.
  • Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula K.E. = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity.
  • Moment of Inertia – A measure of an object's resistance to changes in its rotation, dependent on the mass distribution relative to the axis of rotation.
  • Angular Velocity – The rate of rotation of an object, measured in radians per second (rad/s).
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