Question

(a) A uniform disk of mass 21 kg, thickness 0.5 m, and radius 0.6 m is located at the origin, oriented with its axis along the axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the axis and look toward the origin at the disk). The disk makes one complete rotation every 0.7 s. What is the rotational angular momentum of the disk? What is the rotational kinetic energy of the disk? (Express your answer for rotational angular momentum in vector form.)

Answer 1

Answer:L=33.93

R.E.=152.30

Explanation:

Given

mass of disk$\left ( m\right )$=21kg

thickness$\left ( t\right )$=0.5m

radius$\left ( r\right )$=0.6m

t=0.7 sec for every complete rotation

therefore angular velocity$\left ( \omega \right ) =\frac{\Delta \theta }{\Delta t}$

$\left ( \omega \right )=\frac{ 2\pi }{0.7}=8.977$ rad/s

Rotational angular momentum is given by

$L=I\omega$

$I$=$\frac{mr^2}{2}$

I=3.78 $kg-m^2$

$L=3.78\times 8.977$

L=33.93 $\hat{j}$

considering disk is rotating in z-x plane

Rotational kinetic energy=$\frac{I\omega ^{2}}{2}$=152.30 J