Question

Each of the following objects has a radius of 0.145 m and a mass of 2.60 kg, and each rotates about an axis through its center (as in this table) with an angular speed of 41.8 rad/s. Find the magnitude of the angular momentum of each object.

(a) a hoop kg · m2/s (b) a solid cylinder kg · m2/s

(c) a solid sphere kg · m2/s

(d) a hollow spherical shell kg · m2/s

Answer 1

given

M = 2.6 kg

R = 0.145 m

w = 41.8 rad/s

a) Moment of Inertia of hoop, I = M*R^2

= 2.6*0.145^2

= 0.054665 kg.m^2

angular momentum = I*w

= 0.054665*41.8

= 2.285 kg.m^2/s

b) Moment of Inertia solid sphere, I = (2/5)*M*R^2

= (2/5)*2.6*0.145^2

= 0.021866 kg.m^2

angular momentum = I*w

= 0.021866*41.8

= 0.914 kg.m^2/s

c) Moment of Inertia hallow sphrical sheel, I = (2/3)*M*R^2

= (2/3)*2.6*0.145^2

= 0.036443 kg.m^2

angular momentum = I*w

= 0.036443*41.8

= 1.523 kg.m^2/s