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A spherical shell of radius 1.34 cm and a sphere of radius 7.72 cm are rolling without slipping along the same floor. ?
A spherical shell of radius 1.34 cm and a sphere of radius 7.72 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?
Assignment caught me off guard, due today, helppp (more on the way)
1 Answer
- Dr. ZorroLv 72 years ago
K = 1/2 I ω^2
For a solid sphere of mass m and radius R:
I1= 2/5 m R^2
For a spherical shell of the same mass m and radius r:
I2= 2/3 m r^2
Equal kinetic energy:
1/2 I1 ω1^2 = 1/2 I2 ω2^2
implies
ω2/ω1 = sqrt(I1/I2)
Using the expressions for the moment of inertia:
ω2/ω1= sqrt(3/5) R/r = 4.46
