Question

In: Physics

A disc and solid sphere are both rolling without slipping so that both have a kinetic...

A disc and solid sphere are both rolling without slipping so that both have a kinetic energy of 294. What is the translational kinetic energy of the disc ? What is the translational kinetic energy of the solid sphere ?

Solutions

Expert Solution

Mass of the disc = M1

Radius of the disc = R1

Moment of inertia of the disc = I1 = M1R12/2

Speed of the disc = V1

Angular speed of the disc = 1 = V1/R

Total kinetic energy of the disc = E1 = 294 J

Translational kinetic energy of the disc = E1t

Rotational kinetic energy of the disc = E1r

E1r = 0.5E1t

E1 = E1t + E1r

294 = E1t + 0.5E1t

E1t = 196 J

Mass of the solid sphere = M2

Radius of the solid sphere = R2

Moment of inertia of the solid sphere = I2 = 2M2R22/5

Speed of the solid sphere = V2

Angular speed of the solid sphere = 2 = V2/R

Total kinetic energy of the solid sphere = E2 = 294 J

Translational kinetic energy of the solid sphere = E2t

Rotational kinetic energy of the solid sphere = E2r

E2r = 0.4E2t

E2 = E2t + E2r

294 = E2t + 0.4E2t

E2t = 210 J

A) Translational kinetic energy of the disc = 196 J

B) Translational kinetic energy of the solid sphere = 210 J


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