Question

A disk with a c value of 1/2, a mass of 3 kg, and radius of 0.49 meters, rolls without slipping down an incline with has a length of 9 meters and angle of 30 degrees. At the top of the incline the disk is spinning at 31 rad/s. What is the rotational kinetic energy of the disk at the top of the incline in Joules?

Answer 1

given

m = 3 kg

r = 0.49 m

= 31 rad/sec

the rotational Kinetic Energy is KE = 1/2 I ²

here,

the moment of inertia is

I = 1/2 m r²

KE = 1/2 x 1/2 m r² x ²

= 1/4 m r²²  

= 1/4 x 3 x 0.49² x 31²

KE = 173.052 J

so the rotational kinetic energy of the disk at the top of the incline in Joules is KE = 173.052 J