Force and Acceleration with respect to Circular Motion and the Concept of Pseudo Forces.

Newton’s Three Laws of Motion In order to obtain a full grasp of the relationship that force and acceleration have with circular motion, Newton’s three laws of motion must defined. They are… 1. A particle in motion or at rest will remain in motion or at rest unless a force is acted upon it. 2. A particle’s acceleration is directly proportional to the net force acting on it and inversely proportional to it’s mass. 3. If two particles interact, the force of particle one on particle two is equal and opposite the force of particle two on particle one.

Circular Motion According to Newton’s first law of motion, in a perfect atmosphere where there are no forces, objects are either at rest or at constant velocity. However, this is only true in very few circumstances. Observation reveals that acceleration and deceleration occurs all around us. This brings us to Newton’s second law of motion. Newton’s second law simply states that in order for objects or particles to accelerate there must be a force acting on these particles. This is true for particles in circular motion. There must be a force acting on these objects to cause them to accelerate and decelerate. With this theory as background, the first idea to circular motion is that in circular motion there is velocity and acceleration.

Acceleration and Circular Motion The acceleration in circular motion is given as… a = |v|²/r Where a is acceleration, v is velocity, and r is the radius of the circle. As this equation depicts, the direction of acceleration in circular motion is always in towards the center of the circle because the direction of r is towards the center of the circle. However, it has already been stated that there must be a force that yields this acceleration. This force is presentated as… F = m × a = m × (|v|²/r) From this equation, the direction of force is also towards the center of the circle with respect to circular motion. A good example that will solidify this concept is a car on a racetrack.

Example: Race Track On a race track, the cars are racing around a track that is in a circle - circular motion. As the cars are in motion, the acceleration of the cars pulls them in towards the center of the of the racetrack. Consider the picture below…

A Banked Racetrack In the previous example, imagine that the racetrack would be banked. This would have a noticable effect on the pull of acceleration towards the center of the circle. Examine the picture. The mgsinθ is another one of the forces on the car that will push it towards the center of the racetrack. If the racetrac is banked enough, the driver can keep the steering will straight and still go in a circle around the racetrack.

Psuedo and Fictitious Forces A fictitious or pseudo force is one that is not real but caused by a force that is real. Usually, it is in the opposite direction of the real force. Many times a fictitious force is felt because a person is in an accelerating reference frame. Consider a car decelerating. As the driver applies the brakes, the direction of the actual force is opposite the direction the car would be travelling. However, the driver would experience a force pushing him towards the direction the car is going. This force would be called the pseudo or fictitious force, and the same example would apply for a car accelerating. Pseudo forces are measurable. Watch out for pseudo forces.