Question

A cylinder of radius 1.34 cm and a spherical shell of radius 6.97 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the cylinder's angular speed wcyl to the spherical shell's angular speed wshl be?

Answer 1

Answer:

Explanation:

Moment of inertial of a UNIFORM cylinder is ½mR²

Moment of inertial of a spherical shell is ⅔mR²

Total kinetic energy is

KE = ½mv² + ½Iω²

KE = ½m(Rω)² + ½Iω²

KE = ½mR²ω² + ½Iω²

for the cylinder

KE = ½mR²ω₁² + ½(½mR²)ω₁²

KE = ¾m0.0134²ω₁²

for the sphere

KE = ½mR²ω₂² + ½(⅔mR²)ω₂²

KE = ⅚m0.0697²ω₂²

as the KE and mass are the same

¾m0.0134²ω₁² = ⅚m0.0697²ω₂²

¾0.0134²ω₁² = ⅚0.0697²ω₂²

ω₁²/ω₂² = ⅚0.0697²/¾0.0134²

ω₁/ω₂ = 0.0697√⅚ / 0.0134√¾

ω₁/ω₂ = 5.48285455...