Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies
Show all work for partial credit. Use additional paper if necessary.
Kinematic Equations
1.
The vertical-axis windmill consists of two blades that have a parabolic shape. If
the blades are originally at rest and begin to turn with a constant angular
acceleration of αe = 0.5 rad/s 2, determine the magnitude of the velocity and
acceleration of points A and B on the blade after the blade has rotated through
two revolutions.
Velocity and Acceleration Vectors
2.
At a given instant, the slider block B is traveling to the right
with the velocity and acceleration shown. Determine the
angular acceleration of the wheel at this instant.
Equations of Motion
3.
Determine the acceleration of the block down the plane when
it is released. The block has a mass m, and the cylinder has a
mass M and a radius R. Assume the cylinder does not slip as
it rolls, and the block slides on a smooth surface. The peg at
B is smooth.
MAE-2102
1
Summer 2004
Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies
Principal of Work and Energy
4.
The elevator car E has a mass of 1.80 Mg and the counterweight C has a
mass of 2.30 Mg. If a motor turns the driving sheave A with a torque of
M=(0.06θ2 + 7.5) N*m, where θ is in radians, determine the speed of the
elevator when it has ascended 12 m starting from rest. Each sheave A and B
has a mass of 150 kg and a radius of gyration of k=0.2 m about its mass
center or pinned axis. Neglect the mass of the cable and assume the cable
does not slip on the sheaves.
Conservation of Energy
5.
At the instant shown, the 50-lb bar is rotating downwards at 2
rad/s. The spring attached to its end always remains vertical
due to the roller guide at C. If the spring has an unstretched
length of 2 ft and a stiffness of k=6 lb/ft, determine the
angular velocity of the bar the instant it has rotated
downward 30 degrees below the horizontal.
Principal of Impulse and Momentum
6.
Gear A has a mass of 60 kg and a radius of gyration k C=160mm.
Gear B has a mass of 25 kg and a radius of gyration k D =125
mm. If a motor supplies a torque having a magnitude M=(1.2t)
N*m, where t is in seconds, to gear A, determine the angular
velocity of gear B in 3 s. Initially, gear A is rotating at ω1=2
rad/s.
MAE-2102
2
Summer 2004
Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies
Conservation of Momentum
7.
(19-42) A thin rod of mass m has an angular velocity ω0
while rotating on a smooth surface. Determine its new
angular velocity just after its end strikes and hooks onto
the peg and the rod starts to rotate about P without
rebounding. Solve the problem (a) using the parameters
given, (b) setting m=2 kg, ω0=4 rad/s, l=1.5 m.
Extra Credit
Instantaneous Center of Rotation
Moment of Inertia
MAE-2102
3
Summer 2004