What is the Acceleration of a Spherical Shell Filled with Fluid on an Incline?

[postfan]

Is that right ?

 

[Nathanael]

Ok so 2*M*g*sin(alpha)-F_f=2M*a for forces
and F_f*R=(2/3)*M*R^2*angularacceleration for torque

How's that?

It looks right. Then solve the second equation for the angular acceleration and multiply both sides by R and then plug that expression in for a (because Rα=a like we said) then you can solve for F_f and then you can put F_f back into the original linear acceleration equation to get the answer.

About your earlier question of why friction is necessary: If you placed the ball from rest on a frictionless ramp it would just slide down the ramp without rotating (there would be no torque).

 

[postfan]

So I did that and got a=3/4gsin(alpha). Is that right?

 

[Nathanael]

So I did that and got a=3/4gsin(alpha). Is that right?

Yes

 

[postfan]

Cool thanks for the help and staying up with me last night (till 4:30!).

 

[postfan]

Also did they just give you the moment of inertia for a solid sphere just to trick you?

 

[Nathanael]

Also did they just give you the moment of inertia for a solid sphere just to trick you?

Well, I can't get inside the mind of the test-makers, but if you're asking if that piece of information was irrelevant, then yes, it was irrelevant.

 

[haruspex]

did they just give you the moment of inertia for a solid sphere just to trick you?

Had they given you all the formulae except that one it would have been rather a strong clue.