#17 PLEASE ANSWER ALL PARTS AND SHOW ALL WORK !! THANK YOU A student sits on a r

Question

#17

PLEASE ANSWER ALL PARTS AND SHOW ALL WORK !! THANK YOU

A student sits on a rotating stool holding two 3.4-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg m^2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.23 m from the rotation axis. Find the new angular speed of the student. Your response differs from the correct answer by more than 10%. Double check your calculations, rad/s Find the kinetic energy of the student before and after the objects are pulled in. Your response differs from the correct answer by more than 10%. Double check your calculations.

Explanation / Answer

moment of inertia of tye student plus stool Io=3 kg,m^2

mass of the object m=3.4 kg

initially arms extended r1=1m

finally arms extended r2=0.23 m

initial angular speed w1=0.75 rad/sec

final angular speed is w2

a)

by using law of conservation of momentum,

I1*w1=I2*w2

(Io+2*m*r1^2)*w1=(Io+2*m*r2^2)*w2

==>

(3+2*3.4*1^2)*0.75=(3+2*3.4*0.23^2)*w2

===> w2=2.188 rad/sec

final angular speed w2=2.188 rad/sec

or w2=2.2 rad/sec

b)

initial kinetic enegry K1=1/2*I1*w1^2

K1=1/2*(Io+2*m*r1^2)*w1^2

K1=1/2*((3+2*3.4*1^2)*0.75^2

K1=2.756 J

c)

final kinetic enegry K2=1/2*I2*w2^2

K2=1/2*(Io+2*m*r2^2)*w2^2

K2=1/2*(3+2*3.4*0.23^2)*2.188^2

K2=8.042 J

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