A student sits on a rotating stool holding two 5 kg objects. When his arms are extended horizontally, the objects are 1.1 m from the axis of rotation, and he rotates with angular speed of 0.73 rad/sec. The moment of inertia of the student plus the stool is 2 kg m^2 and is assumed to be constant. The student then pulls the objects horizontally to a radius 0.31 m from the rotation axis.
(a) Calculate the final angular speed of the student. Answer in units of rad/s.
(b) Find the kinetic energy of the student before and after the objects are pulled in.

Explanation:

Given that,

Two object of Mass = 5kg

M1 = M2 = 5kg

Radius of rotation r = 1.1m

Angular speed wi = 0.73rad/s

Moment of inertia I = 2kgm²

The student pull the mass to another position of r' = 0.31m

A. Final angular momentum?

Using the conservation of angular momentum

The momentum of inertia of the objects the students holding I = mr²

L(initial) = L(final)

I•wi = I•wf

(I+mr²+mr²)•wi = (I+mr'²+mr'²)•wf

(2+5•1.1²+5•1.1²)•0.73=(2+5•0.31²+5•0.31²)wf

10.293 = 2.961wf

Then, wf= 10.293/2.961

wf = 3.476 rad/s

wf ≈ 3.48rad/s

b) kinetic energy before and after

Kinetic energy is give as

Kinetic energy = ½•I•w²

Initial kinetic energy is

K.E(initial) = ½(I+mr²+mr²)wi²

K.E(initial) = ½(2+5•1.1²+5•1.1²)•0.73²

K.E(initial) = 3.76 J

Final kinetic energy is

K.E(final) = ½(I+mr'²+mr'²)wf²

K.E(final)=½(2+5•0.31²+5•0.31²)3.48²

K.E(final) = 17.93J

specific latent heat of fusion, lf, of a substance is defined as the amount of heat required to change a unit mass of the substance from solid to liquid state, without any change in the temperature.

explanation:

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft