Angular momentum of different type of spheres
I am curious on why the different type of sphere (for example, a solid wooden sphere vs a hollow sphere) have different angular momentum when they spin. Which one is the one with higher angular momentum? Why?
Answer
First, think about two objects moving in a straight line at the same speed. Which has more linear momentum? The formula is p = mv, so clearly the object with more mass has more momentum.
Now, think about two spinning objects. The formula for angular momentum is L = I ω, where I is the moment of inertia and ω is the angular velocity. From the equation we can see that, of the two objects spinning at the same rate, the one with the higher moment of inertia has more angular momentum.
Moment of inertia is a measure of the distribution of the mass. If more of the mass is farther away from the spin axis, the moment of inertia is higher. So for the case of a solid sphere vs a hollow sphere with the same masses, a hollow sphere has its mass all distributed at the radius whereas the solid sphere is more uniformly distributed. The hollow sphere then has a higher moment of inertia and thus more angular momentum.
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First, think about two objects moving in a straight line at the same speed. Which has more linear momentum? The formula is p = mv, so clearly the object with more mass has more momentum.
Now, think about two spinning objects. The formula for angular momentum is L = I ω, where I is the moment of inertia and ω is the angular velocity. From the equation we can see that, of the two objects spinning at the same rate, the one with the higher moment of inertia has more angular momentum.
Moment of inertia is a measure of the distribution of the mass. If more of the mass is farther away from the spin axis, the moment of inertia is higher. So for the case of a solid sphere vs a hollow sphere with the same masses, a hollow sphere has its mass all distributed at the radius whereas the solid sphere is more uniformly distributed. The hollow sphere then has a higher moment of inertia and thus more angular momentum.