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A solid sphere of mass M and radius R is rolling without slipping on a horizonta

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Question: A solid sphere of mass M and radius R is rolling without slipping on a horizontal surface. What is the expression for its total angular momentum about its center of mass?

Options:

  1. (2/5)MR^2ω
  2. MR^2ω
  3. MR^2
  4. 0

Correct Answer: (2/5)MR^2ω

Solution: 

Total angular momentum L = Iω, where I = (2/5)MR^2 for a solid sphere.

A solid sphere of mass M and radius R is rolling without slipping on a horizonta

Practice Questions

Q1
A solid sphere of mass M and radius R is rolling without slipping on a horizontal surface. What is the expression for its total angular momentum about its center of mass?
  1. (2/5)MR^2ω
  2. MR^2ω
  3. MR^2
  4. 0

Questions & Step-by-Step Solutions

A solid sphere of mass M and radius R is rolling without slipping on a horizontal surface. What is the expression for its total angular momentum about its center of mass?
  • Step 1: Understand that angular momentum (L) is calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity.
  • Step 2: Identify the moment of inertia (I) for a solid sphere, which is given by the formula I = (2/5)MR^2, where M is the mass and R is the radius of the sphere.
  • Step 3: Determine the angular velocity (ω) of the sphere. This is the rate at which the sphere is rotating around its center of mass.
  • Step 4: Substitute the moment of inertia (I) into the angular momentum formula: L = (2/5)MR^2 * ω.
  • Step 5: The final expression for the total angular momentum about the center of mass of the solid sphere is L = (2/5)MR^2ω.
  • Angular Momentum – Angular momentum is the product of the moment of inertia and the angular velocity of an object.
  • Moment of Inertia – The moment of inertia for a solid sphere is given by the formula I = (2/5)MR^2.
  • Rolling Motion – Rolling without slipping involves both translational and rotational motion, affecting the total angular momentum.
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