A student sits on a rotating stool holding two 2.0 kg objects. When his arms are
ID: 1727416 • Letter: A
Question
A student sits on a rotating stool holding two 2.0 kg objects. When his arms are extendedhorizontally, the objects are 1.0 m from the axis of rotation, andhe rotates with an angular speed of 0.75 rad/s. The moment ofinertia of the student plus stool is 3.0 kg·m2and is assumed to be constant. The student then pulls the objectshorizontally to 0.20 m from therotation axis. (a) Find the new angular speed of the student.1 rad/s
(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before 2 J after 3 J before 2 J after 3 J
Explanation / Answer
(a)
from the given problem the total anguar momentum ofthe system of the student the stool and the
weights about the axis of rotation is givenby
Itotal = Iweights +Istudent
= 2 (m r2) + 2.0 kg . m2
intially we get
r = 1.00 m
Ii = 2 (2.0 kg) (1.00 m)2 +3.0 kg . m2
= ........ kg .m2
finally
r = 1.00 m
If = 2 (2.00 kg) (1.00 m)2 +3.00 kg . m2
= ........ kg .m2
according to the law of conservation of momentum weget
If f =Ii i
solve for f
f = ........ rad / s
(b)
KEi = (1 / 2) Iii2
=........ J
KEf = (1 / 2) Iff2
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