49 J is the total kinetic energy. If a bowling ball of mass 7.3 kg and radius 9.6 cm rolls without slipping down a lane at 3.1 m/s. Kinetic energy is the energy an bowling ball has because of its motion.
Given: m = 7.3 Kg ; r = 9.4 cm = 0.094 m ; v = 3.1 m
Now total kinetic energy in this case is given by KE = Kinetic energy due to rotation + Kinetic energy due to translation
i,e KE = 1/2*m*v2 + 1/2*I*ω2 where I is the moment of inertia of the bowling ball about it's center and ω is the angular velocity
Now for pure rotation (without slipping) v = rω
also for the ball (solid sphere) I = 2/5*m*r2
Hence our kinetic energy becomes
KE = 1/2*m*v2 + 1/5*m*v2 = 7/10*m*v2
so KE = 0.7*7.3*(3.1)2 = 49.10 J = 49 J
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