Question

Q.12 A wheel of mass 8 Kg and radius 40 cm is rolling on a horizontal road with angular velocity of 15 rad/s. The moment of inertia of the wheel about its axis is 0.64 kg/m^2. Total kinetic energy of
wheel is *
A)288j
B)216j
C)72 j
D)144j​

Answer 1

Given info :  A wheel of mass 8 Kg and radius 40 cm is rolling on a horizontal road with angular velocity of 15 rad/s. The moment of inertia of the wheel about its axis is 0.64 kg/m².

To find : the total kinetic energy of wheel is ..

solution : total kinetic energy = rotational kinetic energy + translational kinetic energy

= 1/2mv² + 1/2Iω²

for pure rolling, v = ωr

so, K.E = 1/2 m(ωr)² + 1/2Iω²

           = 1/2 ω²(mr² + I)

here m = 8 kg, r = 0.4 m , ω = 15 rad/s and I = 0.64 kg/m²

∴ K.E = 1/2 × 15² (8 × 0.16 + 0.64) = 112.5 × ( 1.28 + 0.64) = 216 J

therefore the total kinetic energy of the wheel is 216 J.