Velocity question?

Question

Which ball (a small golf ball or a bigger ball made out of rubber) would have the bigger velocity when rolled down a hill and why?

Answer 1

If the inertia of the ball is taken into consideration, the golf ball will have a larger linear velocity. This can be modeled by looking at the conversion of potential energy into kinetic energy and rotational energy. Since the rubber ball is larger (bigger r) and I assume a larger mass, more of the potential energy will be converted into rotational energy of that ball versus the golf ball which will has a smaller r and smaller mass.


m*g*h=.5*m*v^2+.5*I*w^2

where I= moment of inertia
w=angular velocity
v=linear velocity
h= height
g=gravity constant

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