Acceleration of hollow sphere rolling down table.

[Bob Loblaw]

Homework Statement

A hollow spherical shell is rolling without slipping or sliding down a board that is tilted at an angle of 35.0° with respect to the horizontal. What is its acceleration?

Homework Equations

I=2/3mr^2

if an object rolls without slipping or sliding:

v = rw

that means that

a = r*alpha

right?

The Attempt at a Solution

I imagine the solution would be something times g sin(35) but I am not sure exactly how to go about solving this one.

 

[Astronuc]

Make sure the moment of inertia is correct.

http://hyperphysics.phy-astr.gsu.edu/hbase/sphinc.html


Now the mass has a force pulling it down the incline, which is the weight component parallel to the incline. The moment of inertia is resisting that force, and the friction prevents the sphere from slipping, so friction is acting at the radius in the direction opposite the translational motion parallel with the plane of the incline.

v = rw
a = r*alpha

are correct.

 

[Bob Loblaw]

Thanks for the help.

I am still a bit murky on this. I know torque=moment of inertia * radial acceleration. I need to find radial acceleration. How can I solve without knowing the torque or the mass of the object? How can I set up the problem in such a way to cancel the mass?

 

[Bob Loblaw]

I solved it:

9.8sin(35)/(1+2/3)

I am still not sure why it worked out that way. Any kind soul care to help me understand this a little better?