Problem 1: Cart 1, moving at velocity v, strikes the identical cart 2, which is at rest. After the collision, cart 1 is moving at 1/3 v. What is the final velocity of cart 2, and is mechanical energy conserved?
Problem 2: The drum on a washing machine starts from rest and accelerates with an angular acceleration of α = 1.2 rad/s2 as it goes into its final spin cycle.
(a) How long does it take to reach its final angular speed of 15 rad/s?
(b) Through what angle does it rotate during this acceleration?
(c) How far does a point on the rim move during this acceleration, given a drum radius of 0.4 m?
Problem 3: A solid bowling ball is spinning at ωi = 15 rad/s about a vertical axis. It has mass m = 8.0 kg, and radius R = 12 cm. A torque τ = -3.0zˆ Nm is applied to this ball. How much time does it take to stop?
Problem 4: A solid sphere of radius R and mass m slides down a hill without rolling from initial height y = h. It reaches level ground at y = 0 and continues sliding: what is its linear speed?
Problem 5: A solid sphere of radius R and mass m rolls down a hill without sliding from initial height y = h. It reaches level ground at y = 0 and continues rolling: what is its linear speed? Compare your answer with that of the previous problem.
Problem 6: To order of magnitude, what is the rotational inertia of
(a) A CD?
(b) A tire from a small farm tractor?
(c) A county-fair Ferris Wheel loaded with large people?
(d) The Earth?
Problem 7: Masses are initially at rest on a frictionless table as shown in figure. The string does not slip on the pulley, which is in the shape of a uniform disk with radius R. All masses, including the pulley, have mass m. Find the speed of the masses when the hanging mass has fallen a distance h.
Problem 8: The first week back after a nice vacation is hard enough without a problem 8. . .Who really needs problem 8 anyway? Take a deep breath, stretch, and go do problem 9.
Problem 9: A rod of length L has a changing mass per length dm/dx = γx.
(a) Calculate the total mass.
(b) Calculate I around an axis through x = 0, and compare with a uniform rod.
(c) Repeat (b) for an axis through x = L, and compare again.
Problem 10: During a particularly long and boring class, you attempt to balance your pencil on its tip. It falls over, of course. What is the angular velocity of the pencil when it hits the desk, assuming that the pencil can be approximated as a uniform rod and the tip does not slip?
Problem 11: A rod of length L has a mass per length given by dm/dx-gx.
a) Calculate the total mass of the rod?
b) Calculate the rotational inertia I around an axis perpendicular to the rod, through x = 0.