A student sits on a rotating stool holding two 3.7-kg objects. When his arms are

Question

A student sits on a rotating stool holding two 3.7-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 · m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.48 m from the rotation axis. (a) Find the new angular speed of the student. rad/s (b) Find the kinetic energy of the student before and after the objects are pulled in.

Explanation / Answer

here,

moment of inertia of stoll and the student , Is= 3 kg.m^2

initial distance of objects , di = 1 m

final distance of the objects from the rotation axis , df = 0.48 m

mass of the objects , mo = 3.7 kg

initial angular speed , wi = 0.75 rad/s

(a)

let the final angular speed be wf

using conservation of angular momentum

Ii*wi = If*wf

( I + m*di^2) * wi = ( I + m*df^2) * wf

( 3 + 3.7 * 1^2) * 0.75 = ( 3 + 3.7*0.48^2) * wf

wf = 1.3 rad/s

the new angular speed of the student is 1.3 rad/s

(b)

kinetic energy before , KEi = 0.5 * Ii*wi^2

KEi = 0.5* ( I + m*di^2) * wi^2

KEi = 0.5 * ( 3 + 3.7 * 1^2) * 0.75^2

KEi = 1.88 J

kinetic energy after the objects are pull in , KEf = 0.5*If*wf^2

KEf = 0.5*( I + m*df^2) * wf^2

KEf = 0.5 * ( 3 + 3.7*0.48^2) * 1.3^2

KEf = 3.26 J

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