Question

The stick-man has just jumped off of the diving board and has an angular velocity of wi = 0.5 rad What will be his angular velocity if he tucks into a disk? Assume that his initial shape is approximated by a slender rod with a length of 1 = 1.8m, and that his final shape is a uniform disk with a diameter of Ø = 0.65 m. Being a stick-man, he has a mass of m = 1 kg. wi 0 = 0.65 m W2 1 = 1.8m

It is also required to draw the kinetic and free body diagrams

Answer 1

Rotational kinetic energy of the 2 states will be the same.

Rotational kinetic energy is given by K.E = 0.5*I*$\omega ^{2}$

=> I1*$\omega ^{2}$1 = I2$\omega ^{2}$2 .

I= Moment of inertia of the body.

$\omega$=Angular velocity.

I1(Rod) = (mL2 )/12 (l = lengthof rod).

I2(disc) = (mr2)/2 (r= radius of disc).

(mL2 )/12 *$\omega ^{2}$1  =  (mr2)/2 * $\omega ^{2}$ 2 .

L=1.8m, r = 0.325m.

$\omega$1 = 0.5 rad/s.

3.24*0.25 / 12 = 0.105/2 * $\omega ^{2}$ 2 .

$\omega ^{2}$2 . = 1.285

$\omega$2 = 1.133 rad/s.

mg mg FBD

In fbd the only forces acting is gravitational force.There are no reaction forces as the body is in air.

an an Kinetic Diagram

There is only an (normal acceleration) since $\omega$ is only present.