Engineering Mechanics II Planar Constant Angular Acceleration & Dependent Motion

Engineering Mechanics II
Practice Exam #2
Planar Constant Angular Acceleration & Dependent Motion
Wheel B has radius RB = 20 cm and is initially rotating at 20
RPM while undergoing a constant angular acceleration of =10
rad/s2 in the same direction. How fast is it rotating at the end of
the 5 seconds? How many revolutions does it make in the 5
seconds? Point P is on wheel B at a distance of 15 cm from the
center. What is the total acceleration vector of point P at the
end of 5 seconds? Wheel A , which has radius R A=10 cm,
contacts wheel B at point C with no slipping. What is the initial
angular speed of wheel A?
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.
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
 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.
Ver. B, Rev 2
Engineering Mechanics II
Practice Exam #2
Planar Rotating Reference Frames
Arm AB has length RAB =0.12 meter. It is rotating clockwise at
a constant rate of A=2 rad/s and is horizontal at the instant
shown. Arm BC has length RBC = 0.1 meter. It is rotating
clockwise at a constant rate of B=3 rad/s and is vertical at the
instant shown. Collar C has a speed measured relative to arm
BC of 4 m/s downward along arm BC, and is accelerating at 5
m/s2 downward, also measured relative to BC. Find the inertial
velocity and acceleration of collar C at this instant. (Assume
total=5 rad/s and total=0 rad/s2
Planar Kinetics: Fixed-Point Rotation
The pendulum shown is comprised of a rod of length 3 feet with a mass
of 0.5 slugs and a disk of radius 0.75 feet and a mass of 0.25 slugs
affixed to the end of the rod. The other end of the rod is fixed on a
vertical wall at point O, and at the instant shown is horizontal and
rotating downward at =8 radians/sec. Find the center of mass of the
pendulum. How fast is the center of mass moving? Find the tangential
and normal acceleration components of the center of mass. Find the
moment of inertia of the pendulum about point O.
Planar Kinetics: Newton’s Law
Determine the acceleration of the center of mass of the cylinder at the instant
shown. 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.
Ver. B, Rev 2