In: Physics
A spherical shell of radius 2.84 cm and a sphere of radius 7.97 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 spherical shell\'s angular speed to the sphere\'s angular speed be?
Mass of the spherical shell = M1
Radius of the spherical shell = R1 = 2.84 cm = 0.0284 m
Moment of inertia of the spherical shell = I1 = 2M1R12/3
Angular speed of the spherical shell = 1
Speed of the spherical shell = V1 = 1R1
Kinetic energy of the spherical shell = KE1
Mass of the sphere = M2
Radius of the sphere = R2 = 7.97 cm = 0.0797 m
Moment of inertia of the sphere = I2 = 2M2R22/5
Angular speed of the sphere = 2
Speed of the sphere = V2 = 2R2
Kinetic energy of the sphere = KE2
The spherical shell and the sphere have same mass.
M1 = M2
The spherical shell and the sphere have same kinetic energy.
KE1 = KE2
Ratio of the spherical shell's angular speed to the sphere's angular speed = 2.572