A student sits on a rotating stool holding two 3.7-kg objects. When his arms are
ID: 1552373 • Letter: A
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 0.50 m from the rotation axis. (A) Find the new angular speed of the student. (B) Find the kinetic energy of the student before and after the objects are pulled in. (Before and After)
Explanation / Answer
Using law of conservation of angular momentum
angular momentum before = angular momentum after
Li = Lf
I1*w1 = I2*w2
I1 = Io + (m*r^2*2) = 3+(3.7*1^2*2) = 10.4 kg-m^2
I2 = Io+(2*m*r1^2) = 3+(2*3.7*0.5^2) = 4.85 kg-m^2
w1 = 0.75 rad/s
Li = Lf
I1*w1 = I2*w2
10.4*0.75 = 4.85*w2
w2 = 1.608 rad/sec is the answer for A)
B) initial Kinetic energy is KEi = (0.5*I1*w1^2) = (0.5*10.4*0.75^2) = 2.925 J
final kinetic energy is KEf = (0.5*I2*w2^2) = (0.5*4.85*1.608^2) = 6.27 J
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