A solid, horizontal cylinder of mass 13.8 kg and radius 1.00 m rotates with an a

Question

A solid, horizontal cylinder of mass 13.8 kg and radius 1.00 m rotates with an angular speed of 7.50 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped vertically onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system. rad/s Need Help? Read It + -13 points SerCP11 8.P.070 My Notes Ask Your Teacl A student sits on a rotating stool holding two 2.8-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 o the student plus stool is 3.0 kg·m2 and is assumed to be constant. The student then pulls the Ob ects ho izontal y t .27 m or 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 before after

Explanation / Answer

1)
let

M = 13.8 kg, R = 1.00 m
wi = 7.50 rad/s

m = 0.25 kg
r = 0.9 m

wf = ?

Apply conservation of angular momentum

If*wf = Ii*wi

wf = Ii*wi/If

= (0.5*M*R^2)*wi)/(0.5*M*R^2 + m*r^2)

= (0.5*13.8*1^2)*7.5/(0.5*13.8*1^2 + 0.25*0.9^2)

= 7.29 rad/s

2)

Apply conservation of angular momentum

If*wf = Ii*wi

wf = Ii*wi/If

= (3 + 2*2.8*1^2)*0.75/(3 + 2*2.8*0.27^2)

= 1.89 rad/s

b) KE_before = (1/2)*Ii*wi^2

= (1/2)*(3 + 2*2.8*1^2)*0.75^2

= 2.42 J

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