- Determine the direction of the angular momentum for the following
- Calculate the angular momentum for the following particles. Find
the angle between the position and the momentum vectors.
(a) r= (4, -5, 3) and p = (1, 4, -2)
(b) r = (1, -2, 3) and p = (7, -1, 1)
(c) r = (0, 2, 0) and p = (1, 0, 0)
- Calculate the angular momentum of a phonograph record (LP)
rotating at 331/3 rev/min. An LP has a radius
of 15 cm and a mass of 150 g. A typical phonograph can accelerate
an LP from rest to its final speed in 0.35 s, what average torque
would be exerted on the LP?
- A cylinder of mass 250 kg and radius 2.60 m is rotating at
4.00 rad/s on a frictionless surface when two more identical non-rotating
cylinders fall on top of the first. Because of friction between
the cylinders they will eventually all come to rotate at the same
rate. What is this final angular velocity?
- In a nightmare you dream that you are a hamster running in
an exercise wheel. Typical hamsters are 300 g and can run at speeds
of 3.2 m/s. A typical exercise wheel has a moment of inertia about
its centre of 0.250 kg-m2. How fast should the wheel
have been rotating in your dream? The radius of the wheel is 12.0
cm. Treat the hamster as a point mass. Hint what was the
angular momentum of the system before the hamster started running?
- A door with width L = 1.0 m and mass M = 15 kg is hinged on
one side so that it can rotate freely. A bullet, as shown, is
fired into the exact centre of the door. The bullet has mass 25
g and a speed of 400 m/s. What is the angular velocity of the
door with respect to the hinge just after the bullets embeds itself
in the door? The door may be treated as a thin rectangular sheet.
The bullet may be treated as a point mass.
- A 150-g piece of playdough slides across a frictionless table
at v = 5.50 m/s. It collides with a disk of radius R = 35.0 cm
and mass M = 2.50 kg which has a fixed frictionless axle. The
playdough stick to the disk. Treat the playdough as a point mass.
(a) If the disk is not rotating initially, what is its angular velocity
after the collision?
(b) What angular velocity would the disk need to have initially, if
the disk stopped completely after the collision?
- A 22-g bug crawls from the centre to the outside edge of a
150-g disk of radius 15.0 cm. The disk was rotating at 11.0 rad/s.
What will be its final angular velocity? Treat the bug as a point
- A cylindrical rod of radius r = 2.00 cm and mass 1.25 kg is
upright on the edge of a rotating disk of mass 10.0 kg and radius
25.0 cm as is shown in diagram (a) below. The system is rotating
at 15.0 rad/s. The rod falls on its side as shown in diagram (b).
Diagrams (c) and (d) present a side view. What is the new angular
velocity of the system? How much work was done in changing the shape
of the object?
- A bicycle tire has a mass of 4.0 kg and a radius of 0.33 m.
If it is rotating at 22 rad/s what is its angular momentum? If
it is used as a gyroscope with a 24 cm long pivot bar, what will
be its precession speed?