Mechanics tutorial_6.doc
1
1.
The diagram shows the plan and elevation of a pluck resting on ice. The pluck receives an
offset horizontal blow P as shown.
The blow is of short duration and the horizontal
component of contact force with the ice is negligible compared with P. Immediately after
the impact, the magnitude of V
G
, the velocity of the centre of mass G, is V
o
. If the mass of
the pluck is m and the moment of inertia about the vertical axis through G is I, determine
the angular velocity after impact.
x
y
a
P
P
G
G
ans:
(mV
o
a/I)k
2.
Two rotors, A and B, having moments of inertia 2.1 and 1.26 kg m
2
respectively, are
mounted on coaxial shafts that are connected by a friction clutch.
Before clutch
engagement, A rotates at 2000rev/min and B rotates at 1000 rev/min in the opposite
direction. During engagement of the clutches, the developed friction couple increases from
zero uniformly with time, and slipping ceases after 7s. Determine the final speeds of the
shafts and the angular displacement of A during the period of clutch slip.
ans:
875 rev/min, 1194 rad
3.
A uniform pole AB of length l and with end A resting on the ground rotates in a vertical
plane about A and strikes a fixed object at point P, where AP=b. Assuming there is no
bounce, show that the minimum length b such that the blow halts the pole with no further
rotation is b=2l/3.
4.
The openlinked chain shown below is prevented from moving by the forked rod R at A.
The coefficient of friction between the chain and the horizontal surface AB is 0.5 and the
surface BC may be taken to be a smooth circular arc of small radius. If the rod R is
removed, determine the speed of the chain when the end D has dropped 1m. Neglect the
motion of the chain inside the pile at A and assume that there are some links left in the pile.
Also assume that the chain does not loose contact with the surface BC.
R
A
B
C
D
2m
2m
ans:
2.316 m/s
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5.
A roundabout can rotate freely about its vertical axis and a child of mass m is standing on
the roundabout at radius R from the axis. The axial moment of inertia of the roundabout is
I
A
. When the angular velocity is
o
the child leaps off and lands on the ground with no
horizontal component of velocity. What is the angular velocity of the roundabout just after
the child jumps?
ans:
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 Spring '09
 GXXY
 Angular Momentum, Moment Of Inertia, Physical quantities, Mechanics tutorial_6.doc

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