Derived Formulas for Uniform Circular Motion

Several formulas can be derived by using some of the force and centripetal formulas. These formulas will be useful in solving many problems involving circular motion.

1.

This equation can be used for banked curves (where the road, for example, is tilted). v is the speed; r is the radius of the turn; g is gravitational acceleration (9.8 m/s²); and θ is the angle of the banking curve.

2.

This equation can be used for finding the speed necessary for an object to oribit a planet (there is only one speed that an object can have in order to remain in orbit with a fixed radius). v is the speed; r is the radius (distance between the center of the planet and the object); G is the universal gravitational constant (6.67259 x 10^-11 N · m²/kg²), and M is the mass of the planet.

3.

This equation can be used for finding the oribital period of an object (satellite) oribiting around a planet (note: this formula can only be used for orbits that are circular, not elliptical). T is the period (in seconds); r is the radius (distance between the center of the planet and the satellite); G is the universal gravitational constant (6.67259 x 10^-11); and M is the mass of the planet.

There are some other useful derived formulas under the vertical circular motion

Related Articles

• Uniform Circular Motion

References and Further Readings

• Cutnell JD,Johnson KW. 2000. Physics. 5th Ed.. (NY): John Wiley & Sons. 1064 p.