1.   What is meant by circular motion and how can we use it in solving numerical problems?

2.   An amusement park ride consists of a ring of radius A from which hang ropes of length l with seat for the riders. There are SIX ropes each with a seat and rider. When the ring is rotating at a constant angular velocity w each rope forms a constant angle theta with the vertical. Let the mass of each rider be m and neglect friction, air resistance, and the mass of the ring, ropes, and seats.
    a. What forces act on any one rider under the constant rotating condition.
    b. Derive and expression for w in terms of A, l, Ø, and the acceleration of gravity g.
    c. Determine the minimum work that the motor that powers the ride would have to perform to bring the system from rest to the constant rotating condition. Express your answer in terms of m, g, l, Ø, and the speed v of each rider.
   

3.   An object whose mass is 0.0050 kg is in simple harmonic motion with a period of 0.40 s and an amplitude of 10.0 mm.

What is:
   (a) its maximum acceleration?
   (b) its acceleration 5.0 mm from its equilibrium position?
   (c) the force on it at that point?

4.   A block weighing 14.0 N, which slides without friction on a 40 degree incline, is connected to the top of the incline by a massless spring of unstrectched length 0.450 m and a spring constant 120 Nm^-1:
   (a) How far from the top of the incline will the block stop?
   (b) If the block is pulled slightly down the incline and released, what is the period of the ensuing oscillations?

5.   A pair of ice dancers do a spin maneuver whereby the female skater travels in a circular path of radius 1.2 meters at a speed of 2.5 ms^-1. Her mass is 55 kg and the other persons mass is 60 kg.
a.) What is the centripetal acceleration of the girl?
b.) What centripetal force must the guy exert?

   If the guy lets the girl go and the girl extends her arms to 0.6 meters and goes into a spin at 3 revolutions per second then:
a.) What is her roational inertia?
b.) What is her angular momentum?
c.) She brings her arms back in to 0.3 m. Now what is her new angular velocity?

6.   A 6 kg mass hangs from a rope wound on a 50 kg wheel which has a radius of 0.5 meters. The mass falls 10 meters in 3 seconds.
    a.) What is the rotational intertia of the wheel.
    b.) What is the linear acceleration of the falling mass.
    c.) What is the angular acceleration of the wheel.
    d.) What torque is given to the wheel?
    e.) What tension is in the rope?

7.   A 10 kg steel ball rests on an incline. The incline is 4 meters high and 12 meters long. It rolls to the bottom in 3 seconds.
    a.) Find the average linear velocity of the ball.
    b.) Find the final velocity of the ball.
    c.) Find the acceleration of the ball.
    d.) Find the PE at the top of the incline.
    e.) Compute the translational and kinetic energy at the bottom of the incline.

8.   A car with an 80 cm diameter wheel starts from rest and accelerates uniformly to a velocity of 20 ms^-1 in 9 seconds.
    a.) What linear distance did it travel?
    b.) What angular distance did it travel?
    c.) What was the angular velocity?
    d.) What was the linear acceleration?
    e.) What was the angular acceleration?

   A car of mass 1500 kg goes round a horizontal circular bend of radius 100 m at a constant speed of 20 ms^-1.

Calculate the resultant force on the car. (2 marks)
In what direction is the resultant force?
Explain what provides the resultant force. (2 marks)