Physics homework #06

1. The frame presented on the figure below consists of 7 rods, each having mass 20 kg and 1 m long.

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(a) Calculate the moment of inertia of the frame for rotation about its lower edge.
(b) If the frame starts from vertical with zero speed and falls over, how fast is the top edge travelling
just before it hits the ground?

2. A certain mass M is free to slide without friction across a horizontal table. This mass is connected

by a light thread to a mass m that hangs over the edge of the table. The connecting thread passes
over a pulley in the shape of a disk with radius R and mass m

p

. Calculate the velocity of the string

after the hanging mass has fallen a distance y

0

starting from rest, provided that the string does not

slip on the pulley edge.

3. For the system described in the previous problem, determine expressions for the acceleration of the

system and tensions in the two segments of the string.

4. In a college physics lab, students measure the moment of inertia of a disk by dropping a sticky clay

ball of known mass on a horizontal rotating disk and observing the decrease in rotation rate. If the
disk is originally rotating at 30 rpm and then slows down to 20 rpm when a small 100 g mass is
dropped on the disk 12 cm from the axis of rotation, what is the moment of inertia of the disk?

5. A horizontal platform in the shape of a circular disk rotates freely in a horizontal plane about a

frictionless vertical axle. The platform has a mass M = 100 kg and a radius R = 2.0 m. A student
whose mass is m = 60 kg walks slowly from the rim of the disk toward its centre. If the angular
speed of the system is 2.0 rad/s when the student is at the rim, what is the angular speed when he
reaches a point r = 0.50 m from the centre?

6. A 5.0-kg ball is dropped from a height of 12.0 m above one end of a uniform bar that pivots at its

centre. The bar has mass 8.0 kg and is 4.0 m in length. At the other end of the bar sits another
5.0-kg ball, unattached to the bar. The dropped ball sticks to the bar after the collision. How high
will the other ball go after the collision?

Maciej Wo loszyn

WFiIS AGH

http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/