In: Physics
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 ?
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