The total initial kinetic energy of the rolling ring is given by, Ki=Krot+KLinear =
1
2
Iω2+
1
2
mv2 =
1
2
mR2(
v
R
)+
1
2
mv2 =mv2 Substitute 10kg for m and 1.5m∕s for v in equation (I) Ki=(10kg)(1.5m∕s)2 =22.5J Now the change in kinetic energy is given by, ∆KE=Kf−Ki =0−22.5J =−22.5J
