An object rolling along a hemispherical bowl

[Momentum09]

Homework Statement

A uniform solid sphere (moment of inertia = 2/5 mr^2) of mass 1.5kg and radius r = 0.473m, is placed on the inside surface of a hemispherical bowl of radius R = 2.77m. The sphere is released from rest at an angle of 66.9 degrees from the vertical and rolls without slipping.
a) How much potential energy has the sphere lost when it reaches the bottom of the bowl?
b) What is the translational velocity of the sphere when it reaches the bottom of the bowl?
c) What is the angular velocity of the sphere when it reaches the bottom of the bowl?

Homework Equations

KE = 1/2 Iw^2. PE = mgh.

The Attempt at a Solution

For part a, do I just do (1.5kg)(9.8)(2.77sin66.9)?
After I find PE, I will just equate it with 1/2 mv^2 to find the translational velocity and 1/2 Iw^2 to find the angular velocity?

Any help is appreciated. Thank you!

 

[olgranpappy]

For part a, do I just do (1.5kg)(9.8)(2.77sin66.9)?
After I find PE, I will just equate it with 1/2 mv^2 to find the translational velocity and 1/2 Iw^2 to find the angular velocity?

Any help is appreciated. Thank you!

part a looks fine. part b is not fine. the total energy initially is PE + KE_trans + KE_rot. this must equal the total final energy PE_f + KE_trans_f+KE_rot_f. Part a is the value of PE and PE_f=0.

thus set PE = KE_trans_f + KE_rot_f

not equal to each individually.

 

[Dick]

And find a relation between the angular velocity and the linear velocity, since it 'rolls without slipping'.

 

[Momentum09]

I got it. Thank you so much!