A student sits on a rotating stool holding two 3.0 kg objects. When his arms are
ID: 1695770 • Letter: A
Question
A student sits on a rotating stool holding two 3.0 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 the objects horizontally to 0.20 m from the rotation axis.
(a) Find the new angular speed of the student.
_______ rad/s
(b) Find the kinetic energy of the student system before and after the objects are pulled in.
before _______ J
after _______ J
I am really having trouble with the setup of this problem and haven't been able to calculate the right answer. I need help figuring out how I should approach this. It would really help to see the problem worked out to have something to compare my work with so I can see where I'm making my mistakes. Thank you!
Explanation / Answer
sol:
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(a)
mass of the holding = m= 3 kg
arms exteneded horizontial distance = r1 = 1m
angular speed when his arms extended = W1= 0.75 rad/s
moment of inertia when his arms are extended = I1 = 3 kg m^2
when his arms pulls brings to 0.2 m from the rotation axis ,
then , the distance between his arms =r2= 1-0.2 =0.8 m
the mass of the holding = 3 kg
then , the momentum of inertia when his arms extended I2= mr2^2
=3(0.8)^2 kg.m^2
=1.92 kg.m^2
as there is no external torque acting on this system ,
the angular momentum of the system will be constantant
i.e L = IW = constant
for two cases i.e before his arms extended later his arms pulled
I1WI= I2W2
I1=3kg .m^2
w1=0.75 rad/s
I2=1.92 kg.m^2
W2= ? = I1W1/I2
= 3(0.75)/1.92
= 4.32 rad/s
(b)
K.E of the student before objects pulled
=1/2* I1*W1^2
=0.5 *3 * (0.75)^2
=0.84 J
K.E the student after the objects pulled
= 1/2 *I2 * W2^2
=0.5* 1.92* (4.32) ^2
= 17.9 or 18 J
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