Question
Calculate the angular momentum and kinetic energy of a solid uniform sphere with a radius of 0.120 m and a mass of 14.0 kg if it is rotating at 6.00 rad/s about an axis through its center..
Answers
MathMate
r=0.12 m
m=14 kg
Moment of inertia of sphere, I
= (2/5)mr<sup>2</sup>
=0.08064 kg-m<sup>2</sup>
Angular velocity, ω
= 6 rad/sec.
Angular momentum, L
= Iω
= 0.48384 kg-m<sup>2</sup>/s.
Rotational kinetic energy, K<sub>r</sub>
= (1/2)Iω<sup>2</sup>
= (1/2)0.08064 6<sup>2</sup> kg-m<sup>2</sup>/s/s
= 1.45152 kg-m<sup>2</sup>/s<sup>2</sup>
m=14 kg
Moment of inertia of sphere, I
= (2/5)mr<sup>2</sup>
=0.08064 kg-m<sup>2</sup>
Angular velocity, ω
= 6 rad/sec.
Angular momentum, L
= Iω
= 0.48384 kg-m<sup>2</sup>/s.
Rotational kinetic energy, K<sub>r</sub>
= (1/2)Iω<sup>2</sup>
= (1/2)0.08064 6<sup>2</sup> kg-m<sup>2</sup>/s/s
= 1.45152 kg-m<sup>2</sup>/s<sup>2</sup>