A 2 kg disk-like wheel 0.3 m in radius, is rolled on a horizontal surface with t

Question

A 2 kg disk-like wheel 0.3 m in radius, is rolled on a horizontal surface with translational kinetic energy of 9 J. The angular velocity is closest to....

1) 6.5 m/s

2. 10.0 m/s

3) 13.3 m/s

4) 16.6 m/s

5) 20 m/s

I do realize the units of the answers do not match what the question is asking. I wrote that problem verbatim which is contributing to my confusion. I can easily solve for the translational velocity (3 m/s) but don't know how to solve for the angular velocity (in rad/s).

** please show your work

Explanation / Answer

m =2 kg, r = 0.3 m , K = 9 J

KE = 0.5mv^2

v = rw

KE= 0.5mr^2w^2

9 = 0.5*2*0.3^2*w^2

w = 10 rad/s

correct option is (2)

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