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?
(2/5)MR^2ω
MR^2ω
MR^2
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.
