# Practice Page

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### 406-L: Vertical Circles 1: Constant Speed

• Topic Cluster: Dynamics
• Topic: Circular Motion
• Objective: Analyze the forces in a vertical circle when speed is constant, for example, the forces on a pilot as he loops over.
• Content: When an object is swung around in a circle, gravity and tension combine to make the centripetal force acting on an object.
• Level: 4

#### BACK to Ladder Circular Motion

These problems involve a person swinging a mass vertically. Vertical circles are good practice for understanding the nature of the centripetal force, because in a vertical circle, the centripetal force is not always equal to the same force. For practice, note that these problems are very similar to elevator problems.

### Principles

• Centripetal Force is the summation of forces in the inward direction on something moving in a circle.
• Centripetal force must be identified as one or more otherwise existing forces, such as gravity, tension, normal force, or friction.
##### The magnitude of centripetal force:

For an object to move in a circle at a constant speed, the magnitude of centripetal force must equal the value:

F_c = \frac{m v^2}{r}

### Forces

In a vertical circle, there are only two forces acting on the mass:

• Gravity:
• Gravity always has direction down
• Gravity always has a magnitude given by $$F_g = mg$$.
• Tension:
• Tension always has the direction inwards, towards the center of the circle.
• Tension is a constraint force. The magnitude of tension will adjust to the situation. You must determine the net force acting on the object first, then determine the tension.