A 8.0 kg cylinder rolls withoutslipping on a rough surface. At an instant when i

Question

A 8.0 kg cylinder rolls withoutslipping on a rough surface. At an instant when its center ofgravity has a speed of 10.0 m/s. (a) Determine the translational kinetic energyof its center of gravity.
J
(b) Determine the rotational kinetic energy about its center ofgravity.
J
(c) Determine its total kinetic energy
J (a) Determine the translational kinetic energyof its center of gravity.
J
(b) Determine the rotational kinetic energy about its center ofgravity.
J
(c) Determine its total kinetic energy
J

Explanation / Answer

a) We know that translational kinetic energy is T =(1/2)mv2 m = mass of the cylinder = 8 kg v = speed = 8 m/s Then T = (1/2)(8kg)*(8m/s)2 = 256 J b) we know that rotational kinetic energy is R=  (1/2)I2 I = MOMENT OF INERTIA OF THE SOLID CYLINDER = mR2/2      Then R =(1/2)( mR2/2)2 We know that v = R Then R = (1/4)mv2              =(1/4)(8kg)*(8m/s)2 = 128 J c) total kinetic energy = T + R = 256 J + 128 J =384 J              =(1/4)(8kg)*(8m/s)2 = 128 J c) total kinetic energy = T + R = 256 J + 128 J =384 J

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