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꜀.

1. Read the question.
2. Draw a diagram showing all the forces acting on the object (no components).
3. Write the statement ΣF = mv²/r.
4. Replace ΣF with all of the given/implied forces involved in the problem.
5. Expand the forces if possible (e.g w = weight = mg).
6. Isolate the variable you are solving for.
7. Input values.

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