Question

A cylinder of mass 8.0 kg rolls without slipping on a horizontal surface. At a certain...

A cylinder of mass 8.0 kg rolls without slipping on a horizontal surface. At a certain instant its center of mass has a speed of 15.0 m/s.

(a) Determine the translational kinetic energy of its center of mass.
J

(b) Determine the rotational kinetic energy about its center of mass.
J

(c) Determine its total energy.

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Homework Answers

Answer #1

(a)

m = mass of the cylinder = 8 kg

v = linear speed of cylinder = 15 m/s

translational kinetic energy is given as

KEtrans = (0.5) m v2

KEtrans = (0.5) (8) (15)2

KEtrans = 900 J

(b)

r = radius of the cylinder

I = moment of inertia of the cylinder = (0.5) mr2

w = angular speed

rotational kinetic energy is given as

KErot = (0.5) Iw2

KErot = (0.5) ((0.5) mr2 ) (v/r)2

KErot = (0.5) (0.5) m v2

KErot = (0.25) m v2

KErot = (0.25) (8) (15)2

KErot = 450 J

c)

total energy is given as

TE = KEtrans + KErot  

TE = 900 + 450

TE = 1350 J

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