ADDITIONAL PROBLEMS: ANGULAR MOMENTUM AND EQUILIBRIUM
1) A light rigid rod 1.00-m in length rotates in the xy plane
about a pivot through the rod’s center. Two particles of masses 4.00 kg
and 3.00 kg are connected to its ends. Determine the angular momentum of
the system about the origin at the instant the speed of each particle is
5.00 m/s.[answer: 17.5 kg-m2/s]
2) A cylinder for which the moment of inertia is I1
rotates about a vertical, frictionless axle with an angular velocity wo.
A second cylinder, this one having a moment of inertia I2 and
initially not rotating drops onto the first cylinder. Since the surfaces
are not frictionless, the two cylinders eventually reach the same angular
velocity w.
a) Calculate w.
b) Show that energy is lost and calculate the fraction of energy lost.
[answer: (I1)/(I1 +
I2) ]
3) A student holds 2 weights each of mass 10.0 kg. When
his arms are extended horizontally, the weights are 1.00 m from the axis
of rotation and he rotates with a speed of 2.00 rad/s. The moment
of inertia of student plus the stool he is sitting on is 8.00 kg-m2
and is assumed to be constant. If the student then pulls the weights
horizontally to 0.250 m from the rotation axis, calculate the following.
a) The final angular speed of the system
b) Calculate the change in the mechanical energy of the system.
[answer: (a) 6.05 rad/s, (b) 113 J]
4) For what value of x will the system below be balanced at
point P such that the normal force at O is zero?(Note: W1 =
20 N, and W2 = 50 N)
5) A ladder with a uniform density and mass m rests against
a frictionless vertical wall at an angle of 60 degrees. The lower
end rests on a flat surface where the coefficient of static friction is
0.40. A student of mass M = 2m attempts to climb the ladder.
What fraction of the length L of the ladder will the student have reached
when the ladder begins to slip? (Hint: find the value of x that keeps the
ladder in equilibrium, any value of x beyond that causes the ladder to
slip).