Worksheet Practice: Uniform Circular Motion
These problems will allow you to practice your knowledge of situations involving uniform circular motion. Each situation begins with a set of givens and is followed by a series of questions. Make sure that your first submissions are, as always, as accurate as possible.

Refer to the following information for the next six questions.

A coin of mass 25 grams is placed 20 cm from the center on a rotating turntable. The coin does not slip while the platform rotates at a constant angular speed of 40 rpm.

 What is the magnitude of the coin's linear velocity in m/sec?

Which of the following answer correctly illustrates the direction of the coin's linear velocity at the instant it is at the position shown in the diagram above?
 What would be the magnitude of the acceleration experienced by the coin?

Which of the following answer correctly illustrates the direction of the coin's acceleration at the instant it is at the position shown in the diagram above?
 If the coefficient of static friction between the coin and the surface is 0.65, what would the greatest rotational speed the turntable could acquire and still have the coin stay in place?

If the first coin were to be replaced with a larger coin made of the same material, which of the following statements is true?

Refer to the following information for the next five questions.

You have completed a lab using a conical pendulum whose length was 75 cm.

During the lab you collected the following data:

mass of whirled rubber ball = 25 grams
40-second trial #1: 50 rev
40-second trial #2: 52 rev
40-second trial #3: 51 rev
mass of suspended washers = 60 grams

 A freebody diagram of the rubber ball will show what two forces acting on the ball?

 During the experiment, the suspended washers supplied the tension. Using the fact that mg = T cos θ, at what angle was the ball being twirled?

 What was the average frequency for your trials?

 Using the fact that the actual twirling radius was r = L sin θ, what was the magnitude of the rubber ball's average velocity during your trials?

 If another series of trials, with the same rubber ball and washers, had been performed but with a shorter radius would you anticipate the tangential velocity of the ball would increase or decease?

Refer to the following information for the next four questions.

A 400 meter radius curve is banked at 12º.

 What would be the two forces acting on a car that is traveling through this banked curve at its critical velocity?

 What force is supplying the centripetal force to keep the car moving in its circular path?

 What is the critical velocity of a car traveling through this curve?

 If a car were to travel at this same speed through a regular flat curve having this same radius, how large would the coefficient of friction need to be to maintain its contact with the road surface?