1. A collar of mass 1 kg is rigidly attached at the mid-point of
a slender rigid arm AB of mass3 kg. The arm is free to rotate about
a pivot at B. The other end A of the rigid arm is also
rigidlyattached to a ring of mass 5kg with the centre of the ring
at B. The motion of the wholeassembly is constrained within a
vertical plane. Knowing that the arm AB is released from restfrom
the position shown and the gravitational acceleration g = 9.81
m/s2, determine
(a) The angular velocity of the whole assembly when the arm AB
has rotated through 90degrees.
(b) The maximum angular velocity of the whole assembly.(c) Will
the maximum velocity of the whole assembly be higher or lower if
the collar is
initially attached closer to the ring instead of locating at the
centre of the arm? Explainhow you arrive at the answer.
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2. The figure below shows a slender rod releasing from rest from
a horizontal datam line. Thelength of the rod AB is l = 1 m with a
mass of 2 kg. An additional mass of 1 kg is attached andfixed to
the centre of the rod at G. The mass of the sliders at A and B can
be assumed to benegligible compared to the mass of the rod as well
as the additional mass fixed to the centreof the rod at G.
Use the energy principle to determine the angular velocity and
the velocity of the centre ofmass G when the centre of the rod G is
0.3 m below the datam line. The gravitationalacceleration g can be
assumed to be 9.81 m/s2and all frictional forces at the sliding
surfacescan be neglected.
