Uniform Circular Motion
Key Concepts
- Velocity in uniform circular motion is constant and is always tangent to the circular path. In other words, it is perpendicular to the radius of the circle.
- Since the direction is always changing, an object in circular motion always has to be accelerating.
- This is called the centripetal acceleration which always points towards the center of the path.
- Centripetal force is the force required to apply the centripetal acceleration.
- Any force can apply the centripetal force necessary to keep an object in circular motion. Some examples are:
- Tension from a string tied to a ball being swung in a circle.
- The normal force from the walls of a bucket being swung in a circle.
- Gravity between the Earth revolving around the Sun.
- Friction between a turning car’s tires and the ground.
- Since the centripetal force must be present, the net force in circular motion problems can never be 0.
Circular Motion Equations
- Velocity = v = x/t = C/t = 2πr/t
- C = circumference
- Centripetal acceleration = a꜀ = v²/r
- Centripetal force = F꜀ = ma꜀ = mv²/r
Solving Circular Motion Problems
Everything is pretty much the same as force problems except v = 2πr/t, a = a꜀, and F = F꜀.
- Read the question.
- Draw a diagram showing all the forces acting on the object (no components).
- Write the statement ΣF = mv²/r.
- Replace ΣF with all of the given/implied forces involved in the problem.
- Expand the forces if possible (e.g w = weight = mg).
- Isolate the variable you are solving for.
- Input values.