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 r^{2}

KE = 1/2 x 1/2 m r^{2} x
^{2}

= 1/4 m r^{2}^{2}

= 1/4 x 3 x 0.49^{2} x 31^{2}

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**

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