Practice Problem Sheet-1
1) Knowing that point A is moving to the right at a constant speed of 20 in/s, determine
the acceleration of (a) point B, (b) point D.
2) The 100 mm radius drum rolls without slipping on a portion of a belt that moves
downward to the left with a constant velocity of 120 mm/s. Knowing that at a given
instant, the velocity and acceleration of the centre A of the drum are as shown,
determine the acceleration of point D.
3) Knowing that crank AB rotates about point A with a constant angular velocity of 900
rpm clockwise, determine the acceleration of the piston P when θ = 60°.
1
4) Arm AB has a constant angular velocity of 16 rad/s counter-clockwise. At the instant
when θ = 90°, determine the acceleration of (a) collar D, (b) the midpoint G of bar BD.
5) A straight rack rests on a gear of radius r = 3 in. and is attached to a block B as shown.
Knowing that at the instant shown θ = 20°, the angular velocity of gear D is 3 rad/s
clockwise, and it is speeding up at a rate of 2 rad/s2, determine (a) the angular
acceleration of AB, (b) the acceleration of block B.
6) Two rotating rods are connected by slider block P. The rod attached at A rotates with a
constant clockwise angular velocity 𝜔𝐴 . For the given data, determine for the position
shown (a) the angular velocity of the rod attached at B, (b) the relative velocity of slider
block P with respect to the rod on which it slides. Take b = 8 in., 𝜔𝐴 = 6 rad/s.
2
7) Pin P is attached to the wheel shown and slides in a slot cut in bar BD. The wheel rolls
to the right without slipping with a constant angular velocity of 20 rad/s. Knowing that
x = 480 mm when θ = 0, determine the angular velocity of the bar and the relative
velocity of pin P with respect to the rod when (a) θ = 0, (b) θ = 90°.
8) Four pins slide in four separate slots cut in a circular plate as shown. When the plate is
at rest, each pin has a velocity directed as shown and of the same constant magnitude
u. If each pin maintains the same velocity relative to the plate when the plate rotates
about O with a constant counter-clockwise angular velocity ω, determine the
acceleration of each pin.
9) At the instant shown, the length of the boom AB is being decreased at the constant rate
of 0.2 m/s and the boom is being lowered at the constant rate of 0.08 rad/s. Determine
(a) the velocity of point B, (b) the acceleration of point B.
3
10) Pin P slides in a circular slot cut in the plate shown at a constant relative speed u = 90
mm/s. Knowing that at the instant shown the plate rotates clockwise about A at the
constant rate ω = 3 rad/s, determine the acceleration of the pin if it is located at (a) point
A, (b) point B, (c) point C.
11) The blade assembly of an oscillating fan rotates with a constant angular velocity 𝛚𝟏
= − 450 i rpm with respect to the motor housing. Determine the angular acceleration of
the blade assembly, knowing that at the instant shown the angular velocity and the
angular acceleration of the motor housing are, respectively, 𝛚𝟐 = − 3 j rpm and 𝛼2 = 0.
12) The rotor of an electric motor rotates at the constant rate 𝜔1 = 1800 rpm. Determine the
angular acceleration of the rotor as the motor is rotated about the y axis with a constant
angular velocity 𝜔2 of 6 rpm counter-clockwise when viewed from the positive y axis.
4
13) A 3-in. radius disk spins at the constant rate 𝜔2 = 4 rad/s about an axis held by a housing
attached to a horizontal rod that rotates at the constant rate 𝜔1 = 5 rad/s. For the position
shown, determine (a) the angular acceleration of the disk, (b) the acceleration of point
P on the rim of the disk if θ = 0, (c) the acceleration of point P on the rim of the disk if
θ = 90°.
14) The circular plate shown rotates about its vertical diameter at the constant rate 𝜔1 = 10
rad/s. Knowing that in the position shown the disk lies in the XY plane and point D of
strap CD moves upward at a constant relative speed u = 1.5 m/s, determine (a) the
velocity of D, (b) the acceleration of D.
5