A solid cylinder of mass 10.0 kg rollswithout slipping on a horizontal surface.

Question

A solid cylinder of mass 10.0 kg rollswithout slipping on a horizontal surface. (a) At the instant its center of mass has aspeed of 8.0 m/s, determine thetranslational kinetic energy of its center of mass.
1 J

(b) What is the rotational kinetic energy about its center ofmass?
2 J

(c) What is its total energy?
3 J (a) At the instant its center of mass has aspeed of 8.0 m/s, determine thetranslational kinetic energy of its center of mass.
1 J

(b) What is the rotational kinetic energy about its center ofmass?
2 J

(c) What is its total energy?
3 J

Explanation / Answer

Linear speed v = 8 m / s

Mass m = 10 kg

Translational kinetic energy K = ( 1/ 2) mv ^ 2

                                                  = 320 J

(b). Rotational kinetic energy K ‘ = ( 1/ 2) I w^2

            K ‘ = ( ½) (1/ 2) mR ^ 2 ( v^ 2 / R ^ 2 )

                  = ( 1/ 4 ) m v ^ 2

                  = 160 J

(c). Total energy  = K + K ‘= 480 J

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