Physics circular motion

Normal Force: The force acting on the object from the wall of the track, which keeps it moving in a circular path.
- The normal force changes the direction of the object's velocity, keeping it pointed inward toward the center of the circle.
- If the object loses contact with the wall (normal force), it will stop moving in a circle and will not accelerate since there are no forces acting on it horizontally.

When an object is spun (e.g., a ball on a string) and then released, it appears to fly away in a curved path due to the observer's perspective (rotating frame of reference).
- From the observer’s perspective, the object moves straight, illustrating how motion can appear different based on the frame of reference.

Acceleration Direction: When analyzing the forces acting on a car moving at constant speed over the top of a hill, the acceleration must point inward (downward toward the center of the circle).
Force Diagram: At the top of the hill:
- The total force must point down, which includes:
  - Force of gravity pulling down (greater than or equal to the normal force).
  - The normal force from the road, which must be less than the gravitational force since the car is in circular motion.

Understanding that:
- If acceleration points inward, net force also points inward (toward the center of the circle).
- Application of Newton's Second Law: $F_{ ext{net}} = m imes a$ where
  - Letting acceleration, $a = rac{v^2}{r}$, we can derive the net force involved in circular motion.

On a flat surface:
- If an object is moving at a constant speed, there are no forces acting in the horizontal direction.
- No left/right or upward/downward acceleration happens.
- Static Friction: Keeps the vehicle from slipping, along with some air resistance.
As the car moves over the top of a hill:
- The velocity changes direction, indicating there is an acceleration involved even though the speed is constant.

Elevator Example: When an elevator moves up and slows down, the forces acting on a person can illustrate similar principles of acceleration and net forces:
- Tension vs. force of gravity, where tension is less than gravitational force when decelerating.
- Feeling lighter or a push up due to differing normal forces and acceleration effects.

Magnitude of Force of Gravity: Use the formula $F_g = mg$ where:
- Mass of the car ($m = 1,500 ext{ kg}$) and gravitational acceleration ($g = 9.8 ext{ m/s}^2$).
- Resulting force of gravity is $F_g = 1,500 ext{ kg} imes 9.8 ext{ m/s}^2 = 14,700 ext{ N}$.
Direction of the Net Force: At the top, net force must also point downward:
- Since acceleration points downward (toward the center of the circle), $F_{ ext{net}} = mb^2/r$ can be utilized to calculate net force downward.
- Example given: If $ ext{speed} = 20 ext{ m/s}$, radius = 60m, then:
  - $F_{ ext{net}} = 1,500 ext{ kg} imes rac{(20 ext{ m/s})^2}{60m} = 10,000 N$.
  - Therefore, $F_{ ext{net,y}} = -10,000 N$ (as it points downward).

Total downward force (net force) = 10,000 N down.
Force of gravity = 14,700 N down.
Using balance of forces:
- Directional comparison gives the normal force as:
  - $F{ ext{normal}} + 10,000 = 14,700 ightarrow F{ ext{normal}} = 4,700 ext{ N (up)}$.

For circular motion and problems involving forces, setting one axis toward the center of the circle can simplify calculations and analysis of forces.
Recap of fundamental elements:
- Acceleration points toward center of the circle for circular motion.
- Use appropriate equations of motion (e.g., $a = rac{v^2}{r}$) to assist in understanding dynamics of circular movements.