explain A student sits on a freely rotating stool holding two dumbbells, each of

Question

explain

A student sits on a freely rotating stool holding two dumbbells, each of mass 3.00 Kg (see figure below). When his arms are extended horizontally (figure a), the dumbbells are 1.01 m from the axis of rotation and the student rotates with an angular speed of 0.755 rad /s. the moment of inertia of the student plus stool is 2.58 kg^2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position to a position 0.304m from the rotation axis (figure b). (a) Find the new angular speed of the student. (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward.

Explanation / Answer

I = 2.58 kg.m^2, m = 3kg , r1 = 1.01m , r2 =0.304 m, w1 =0.756 rad/s

(a) From conservation of angular momentum I1w1 =I2w2

[I+2mr12]w1 =[I+2mr22]w1

[2.58+(2*3*1.01*1.01](0.756)= [2.58+(2*3*0.304*0.304)]w2

6.58 =3.13 w2

w2 =6.58/3.13 = 2.1 rad/s

New angular velocity =2.1 rad/s

(b) Ki = (1/2)I1w12 = L1w1/2 = (6.58*0.756)/2

Ki =2.49 J

Kf = (1/2)I2w2^2 =L2w2/2 = (6.58*2.1)/2

Kf =6.91 J

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