1. A car travels three-quarters of the way around a circle of radius 20.0 m. Its

Question

1. A car travels three-quarters of the way around a circle of radius 20.0 m. Its average velocity for the trip is 7.8 m/s. What was the tangential velocity of the car?

2. A coin is placed on a flat turntable, a distance 5.9 cm from the center of rotation. The coefficient of static friction between the turntable and the coin is 0.2.

At what maximum angular speed may the turntable be rotating before the force of friction is not able to keep the coin at the same distance from the axis?

Hint: if you think a critical piece of information is missing, assign it a letter, and see if it cancels in the end.

Explanation / Answer

Part 1.) The average velocity is defined as: Displacement / Time

Now for three-fourths around the circle the displacement would be: Rcos45

So the time taken = Displacement / Average velocity = (20 / Cos45) / 7.8 = 3.626 Seconds

Now the distance travelled would be the length of the curve.

That is, distance = 0.75 x 2 x 3.14 x 20 = 94.2 m

Therefore the speed of the car = Distance / Time = 94.2 / 3.626 = 25.979 m/s which is the required velocity.

Part 2.) For the coin to be placed on the turn table, a centripetal force is provided by the friction which enables the coin to stay in the circular motion.

Now the force acting on the coin due to friction = Mg

Also, the centripetal force for the motion with angular velocity, say , would be given as: M2R

For the coin to stay in motion and not slip away the above two expressions must be same.

That is: Mg = M2R

or, 2R = g

or, = 5.767 rad/second.

Therefore the required value for the angular speed of the turntable is 5.767 rad/sec

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