# Angular velocity acceleration

1. a solid sphere (I=0.4mr^2) of mass 1.5 kg and radius 15 cm moves down a 35 degrees incline 7m long. Assuming it started from rest, what is its angular velocity in rad/s at the bottom of the incline? a)71.27 b)32.25 c)49.98 d)61.69

3.i tried by plugging in the values and trying to find the angular acceleration so i could use the L=I(angular velocity) equation; but my numbers just dont add up. pls guide me through the process

thnx

ty

Use the principle of conservation of Energy. The gravitational potential energy is converted into Angular Kinetic Energy.

The gravitational potential energy is converted into angular KE AND translational KE. Assuming that rolling without slipping happens here, you can use the relation v=rw to solve for the angular velocity.

can someone pls provide me with a mathematical representation of the previous replies?

or at least outline the steps that i will need to follow

im a bit confused about all this

thnx

ty