Question #b5600

1 Answer
Aug 22, 2017

Total Kinetic Energy = Translational K.E + Rotational K.E = 0.35 J

Explanation:

Velocity v=0.5 ms^-1v=0.5ms1
Angular Velocity omega = v/r = 0.5/0.2 = 2.5 rads^-1ω=vr=0.50.2=2.5rads1
Moment of Inertia of Sphere I = 2/5 MR^2 = 2/5(2kg)(0.2m)^2 = 0.032 kg m^2I=25MR2=25(2kg)(0.2m)2=0.032kgm2

Total Kinetic Energy = Translational K.E + Rotational K.E = 1/2 MV^2 + 1/2 Iomega^212MV2+12Iω2 = 1/2 (2 kg)(0.5ms^-1)^2 + 1/2 (0.032 kg m^2)(2.5 rads^-1)^212(2kg)(0.5ms1)2+12(0.032kgm2)(2.5rads1)2 = 0.35 J