Calculate the rotational kinetic energy for the following objects spinning about

Question

Calculate the rotational kinetic energy for the following objects spinning about a central axis (in units of Joules): a solid sphere with a mass of 100 grams and a radius of 5.0 cm rotating with an angular speed of 2.0 rad/sec. a thin spherical shell with a mass of 100 grams and a radius of 5.0 cm rotating with an angular speed of 2.0 rad/sec. a solid cylinder with a mass of 100 grams and a radius of 5.0 cm rotating with an angular speed of 2.0 rad/sec. a hoop with a mass of 100 grams and a radius of 5.0 cm rotating with an angular speed of 2.0 rad/sec.

Explanation / Answer

Rotational kinetic energy K = 0.5*Iw^2

m = 100 gm , r = 5 cm , w = 2rad/s

a) moment of inertia of solid sphere I = (2/5)mr^2

K = 0.5*(2/5)mr^2*w^2

K = 0.5*(2/5)*0.1*0.05^2*2^2

K =0.002 J

(b) moment of inertia of spherical shell I = (2/3)mr^2

K = 0.5*(2/3)mr^2*w^2

K = 0.5*(2/3)*0.1*0.05^2*2^2

K =0.00033 J

(c) moment of inertia of solid cylinder I = (1/2)mr^2

K = 0.5*(1/2)mr^2*w^2

K = 0.5*(1/2)*0.1*0.05^2*2^2

K =0.00025 J

(d) moment of inertia of hoop I = mr^2

K = 0.5*mr^2*w^2

K = 0.5*0.1*0.05^2*2^2

K =0.0005 J

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