Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies Kinematic Equations

Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies
Show all work for partial credit. Use additional paper if necessary.
Kinematic Equations
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/s2, determine the magnitude of the velocity and
acceleration of point A on the blade after the blade has rotated through two
Velocity and Acceleration Vectors
At a given instant, the slider block B is traveling to the right
with the velocity and acceleration shown. Determine the
angular velocity and acceleration of the wheel at this
instant. The radius of the wheel is 5 inches.
Equations of Motion
Determine the acceleration of the cylinder. The tension in the rope is 12 N. The
cylinder has a mass of 4 kg, and a radius of 0.02 m. Assume the cylinder does not
slip as it rolls.
Conservation of Energy
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.
R. Gist (Sum. ’06)
1 of 2
Ver. B, Rev. 1
Dynamics: Practice #2 Kinematics & Kinetics of Rigid Bodies
Principal of Work and Energy
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=15 N*m, where θ is in radians, determine the speed of the elevator when
it has ascended 14 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.
Principal of Impulse and Momentum
Gear A has a mass of 60 kg and a radius of gyration kC=160mm.
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 A in 3 s. Initially, gear A is rotating at ω1=2 rad/s.
Conservation of Momentum
A thin rod of mass 2kg and length l=1.5 m has an angular
velocity ω0 = 4 rad/s 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.
R. Gist (Sum. ’06)
2 of 2
Ver. B, Rev. 1