Circular Motion

# Pre-Lab Questions

1. In this lab, you will be rotating a mass on one side of a string that is balanced by a second mass on the other end of the string (Figure 5). Apply Newton’s Second Law of Motion to mass 1, *m1*, and mass 2, *m2*, to solve for the period of mass 1.

a. __Hint:__ assume *m1*= 4*m2*. How is the centripetal force on *m1 *related to the force of gravity on *m2*?

*Figure 5: Rotating mass.*

2. Draw a free body diagram and solve for the centripetal acceleration in terms of θ and *g* for one person riding on the amusement park ride in Figure 3.

3. The around the world yo-yo trick is completed when you twirl a yo-yo in a vertical circle. If the yo-yo was in uniform circular motion, compare the force of tension at the top of the circle to the force of tension at the bottom of the circle.

a. __Hint__: Drawing a free body diagram will be helpful.

## Experiment 1: Balancing Centripetal Force

### Data Sheet

Table 1. Rotational Data

Radius (m) | Time per 15 revolutions (s) | Period (s) | Expected Value | Percent Error (%) |

0.25 | | | | |

0.40 | | | | |

0.15 | | | | |

### Post-Lab Questions

1. Compare your measured data to your predicted values with a percent error calculation. Explain any differences with an error analysis.

2. List all of the physical quantities that affect the value of centripetal force.

3. How did the period of rotation vary as you changed the radius?

4. Draw a circle to represent the path taken by your rotating mass. Place a dot on the circle to represent your rotating washer. Add a straight line from the dot to the center of the circle, representing the radius of rotation (the string). Now label the direction of the tangential velocity and the centripetal force.

5. Refer to the picture in Figure 3 again (pictured below). Before the apparatus begins to spin the wires connecting the swings to the top of the structure will be completely vertical. Once the apparatus begins to spin the swings move outward radially, but also upwards vertically. From where does the force causing this vertical acceleration come?

*Figure 3: Swings at an amusement park exhibit a circular path of motion.*

©eScience Labs, 2018

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