How Do You Calculate Angular Velocity of a Sphere on an Incline?

[tahyus]

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 don't add up. pls guide me through the process

thnx

ty

 

[Harmony]

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

 

[chaoseverlasting]

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.

 

[tahyus]

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