Moment of inertia for ball rolling up a ramp.

AI Thread Summary
The discussion centers on calculating the moment of inertia for a non-uniform ball rolling up an incline. The initial parameters include a mass of 1.0 kg, a radius of 0.20 m, and a speed of 10 m/s. The moment of inertia formula I=(2/5)mr^2 is mentioned but deemed inappropriate for a non-uniform sphere. Participants suggest using conservation of energy principles to approach the problem instead. The conversation emphasizes the need to apply the correct methods for non-uniform objects in physics calculations.
azurken
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Homework Statement


A ball with mass 1.0 kg and radius 0.20m rolls without slipping along level ground with a speed of 10 m/s. The ball then rolls up an incline reaching a maximum vertical height of 8.0 m. What is the moment of inertia of the ball? (Do not assume the ball is a uniform sphere).

m=1.0kg
r=0.20m
v=10m/s

Homework Equations


I=(2/5)mr^2


The Attempt at a Solution


Since I really have no clue on where to start this one. I guess I'll focus in on that since it's not a uniform sphere I can still assume it's a ball and use the above formula to plug it in and solve it right?

It comes out to 0.016
 
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azurken said:

Homework Equations


I=(2/5)mr^2


The Attempt at a Solution


I guess I'll focus in on that since it's not a uniform sphere I can still assume it's a ball and use the above formula to plug it in and solve it right?

No, the formula you stated is only valid for a uniform solid sphere. So, you can't assume the formula applies in this problem.

Think of a general important principle that you could use to solve this problem.
 


Conservation of energy?
 


Yes.:smile: Give it a try.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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