# A-level Physics (Advancing Physics)/Circular Motion/Worked Solutions

**1. A tennis ball of mass 10g is attached to the end of a 0.75m string and is swung in a circle around someone's head at a frequency of 1.5Hz. What is the tension in the string?**

**2. A planet orbits a star in a circle. Its year is 100 Earth years, and the distance from the star to the planet is 70 Gm from the star. What is the mass of the star?**

100 days = 100 x 365.24 x 24 x 60 x 60 = 3155673600s

**3. A 2000kg car turns a corner, which is the arc of a circle, at 20kmh ^{-1}. The centripetal force due to friction is 1.5 times the weight of the car. What is the radius of the corner?**

20kmh^{-1} = 20000 / 3600 = 5.56ms^{-1}

This is a bit unrealistic, I know...

**4. Using the formulae for centripetal acceleration and gravitational field strength, and the definition of angular velocity, derive an equation linking the orbital period of a planet to the radius of its orbit.**

So, orbital period squared is proportional to radius of orbit cubed. Incidentally, this is Kepler's Third Law in the special case of a circular orbit (a circle is a type of ellipse).