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# circular motion

1. A ball moves with a constant speed of 4 m/s around a circle of radius 0.25 m. What is the period of the motion?
2. A racecar is traveling at constant speed around a circular track. What happens to the centripetal acceleration of the car if the speed is doubled?
3. A car traveling at 20 m/s rounds to a curve so that its centripetal acceleration is 5 m/s2. What is the radius of the curve?

The world's largest Ferris wheel with a radius of 50.0 m is located in Yokohama city, Japan. Each of the sixty gondolas on the wheel takes 1.00 minute to complete one revolution when it is running at full speed.
4. what is the uniform speed of a gondola when the Ferris wheel is running at full speed?
5. What is the centripetal acceleration of the gondola when the Ferris wheel is running at a full speed?

6. A 0.25-kg ball attached to a string is rotating in a horizontal circle of radius 0.5 m. If the ball revolves twice every second, what is the tension in the string?

7. A certain string just breaks when it is under 400 N of tension. A boy uses this string to whirl a 10-kg stone in a horizontal circle of radius 10m. The boy continuously increases the speed of the stone. At approximately what speed will the string break?

8. In an amusement park ride, a small child stands against the wall of a cylindrical room that is then made to rotate. The floor drops downward and the child remains pinned against the wall. If the radius of the device is 2.15 m and the relevant coefficient of friction between the child and the wall is 0.400, with what minimum speed is the child moving if he is to remain pinned against the wall?

9. Which force is responsible of holding a car in a frictionless banked curve?

10. Which force is responsible of holding a car in a unbanked curve?

#### Solution Preview

1. The perimeter of the circle is
The period is the time for the ball to finish on circle, so