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If the moment of inertia of a body is 10 kg m², what is the rotational kinetic e

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Question: If the moment of inertia of a body is 10 kg m², what is the rotational kinetic energy when it rotates with an angular velocity of 5 rad/s?

Options:

  1. 125 J
  2. 50 J
  3. 100 J
  4. 75 J

Correct Answer: 125 J

Solution: 

Rotational kinetic energy is given by KE = 1/2 I ω² = 1/2 * 10 * 5² = 125 J.

If the moment of inertia of a body is 10 kg m², what is the rotational kinetic e

Practice Questions

Q1
If the moment of inertia of a body is 10 kg m², what is the rotational kinetic energy when it rotates with an angular velocity of 5 rad/s?
  1. 125 J
  2. 50 J
  3. 100 J
  4. 75 J

Questions & Step-by-Step Solutions

If the moment of inertia of a body is 10 kg m², what is the rotational kinetic energy when it rotates with an angular velocity of 5 rad/s?
  • Step 1: Identify the formula for rotational kinetic energy, which is KE = 1/2 I ω².
  • Step 2: Substitute the given moment of inertia (I = 10 kg m²) into the formula.
  • Step 3: Substitute the given angular velocity (ω = 5 rad/s) into the formula.
  • Step 4: Calculate ω², which is 5² = 25.
  • Step 5: Multiply I (10 kg m²) by ω² (25) to get 10 * 25 = 250.
  • Step 6: Multiply the result by 1/2 to find KE: 1/2 * 250 = 125 J.
  • Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula KE = 1/2 I ω², 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.
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