1. Derivation of the proportionality of velocity and radius for an object in circular motion under a constant centripetal force.

2. 45 degree angle To ensure a constant centripetal force the angle with the vertical is kept at a constant 45 degrees.

3. Horizontal Using Newton’s 2 nd law in the horizontal direction

4. The only force on the body horizontally is the horizontal force of tension in the string and the acceleration is centripetal and towards the center.

5. Vertical Using Newton’s 1 st law in the vertical direction

6. The vertical component of the tension on the string is pulling up and gravity is pulling down.

8. Substitute this expression into the equation for the horizontal dimension

11. Substitute for the weight at the earth’s surface, simplifying and solving for v.