Unit 3: Circular Motion and Gravitation

Executive Summary

Circular motion needs a center-pointing net force; gravitation supplies it for orbits, and Newton's law of gravitation quantifies the pull.

Centripetal acceleration and force

An object in uniform circular motion accelerates toward the center with $a_c = \frac{v^2}{r}$. The centripetal "force" is the NET force toward the center — gravity, tension, friction, or the normal force can all play the role; it is never an extra force on the diagram.

Universal gravitation

$F_g = G\frac{m_1 m_2}{r^2}$, and the gravitational field is $g = \frac{GM}{r^2}$. Orbital speed follows $v = \sqrt{\frac{GM}{r}}$; Kepler's third law (periods squared proportional to orbital radii cubed) falls out of the same force.

Applications

Vertical circles: tension is largest at the bottom and smallest at the top (minimum top speed to stay in the circle). Banked curves use the normal force's horizontal component. Satellites and astronauts are in free fall — "weightlessness" is just falling around Earth.

Exam traps

The centripetal force is not a separate force to add. If the force is removed, the object moves in a straight line tangent to the circle (Newton's first law), not outward. Gravitational force depends on 1/r², so doubling distance quarters the force — ratio questions hinge on this.