## Circular Motion Concepts

**True:**Your apparent weight is greater than mg when moving in an elevator that is accelerating upward.

**True:**In order for an object to travel in a circle, a force must be applied on the object that points towards the center of the circle

**False:**The magnitude of the gravitation force exerted by the Earth on the Moon is greater than the Moon exerts on the Eart

**True:**An astronaut is weightless in the space shuttle because both astronaut and the shuttle have the same acceleration

**True:**Water is removed from clothes in a spin dryer in the direction that is tangential to the circle

## **Approach**

Newton's Law of Gravitation states that...

F=G*(m1m2/r^2)

F=G*(m1m2/r^2)

- This is the force that m1 (Earth) exerts on m2 (the Moon). It is also the force that m2 exserts on m1. But you knew that from Newton's Third Law of Motion - "for every force there is an
**equal**and opposite reaction force." - The force necessary to make an object move in a circle is toward the center of the circle. Newton's First Law of Motion states that an object remains at rest or moves along at a constant velocity unless act upon by a force. An object moving in a circle changes direction constantly - in the direction toward the center. This implies that a force is needed in the same direction.
- Once a ball is released from a circular motion it will move in the tangential direction. This is because when released there is no force acting on it and Newton's First Law of Motion states that an object remains at rest or moves along at a constant velocity unless act upon by a force.
- The apparent weight is determined by the normal force (the elevator floor on your feet). Taking up to be positive then

- since W = mg and g = +9.81 m/s2. So if the elevator is accelerating downwards, a < 0 giving FN < mg. If the elevator is accelerating upwards then a > 0. In this case FN > mg. If the acceleration/deceleration is not given then the statement is undetermined.