Circular Motion at Constant Speed

Main Ideas

There are two main ideas pertaining to circular motion at constant speed.

  1. The acceleration, and therefore the net force on the object, is directed toward the center and has a constant magnitude of

    Symbolic::Image("a_(rad)=(v^2)/r")

    The subscript rad is a reminder that the acceleration is radial, meaning that it is directed toward the center of the circle.

  2. The velocity is always tangent to the path and has a magnitude equal to

    Symbolic::Image("v=(2 pi r)/T")

    where T, the period of the motion, is the time interval for the object to make one complete revolution.

Checkpoint

1. A point on a rotating wheel is shown in the animation below.

(a) To measure the radius of the wheel, click on the animation and read the coordinates of your mouse click. The units of position and time are meters and seconds, respectively. What is the speed of the red point on the wheel? v = <_> m/s

(b) What is the magnitude of the acceleration of the red point on the wheel? arad = <_> m/s2

(c) What would be your answers to (a) and (b) for a point that is halfway from the center of the wheel to the edge along a spoke? Click here to see that point.

v = <_> m/s     arad = <_> m/s2

For an object to travel in circular motion at constant speed, the net force on the object must be in the radial direction. Remember that the net force is the sum of all of the forces acting on the object. This means that the tangential components of all of the forces on the object must sum to zero, so that the net force is in the radial direction.

One or more forces on an object are responsible to maintaining the net force needed for an objet to travel in circular motion at constant speed. For each o the following scenarios, which forces act in the radial direction and are principally responsible for the motion of the object?

  • You tie a tennis ball to a string and whirl it above your head? [The force of the string on the ball (i.e. tension)]
  • A car rounds a circular turn on a flat road at constant speed? [Friction of the road on the tires that acts perpendicular to the tred of the tire and toward the center of the circle.]
  • You ride in a vertical circle at constant speed on a Ferris Wheel and are at the top of the circle. [The radial component of the net force in this case is the gravitational force of the earth on you minus the upward component of the force of the seat on you (or Weight minus Normal force).]
  • You ride in a vertical circle at constant speed on a Ferris Wheel and are at the bottom of the circle. [The radial component of the net force in this case is the upward component of the force of the seat on you minus the gravitational force of the earth on you (or Normal force minus Weight).]
  • A satellite is in a circular orbit at constant speed around the Earth. [The gravitational force of the Earth on the satellite.]
  • An airplane "banks" in a horizontal circular turn at constant speed. [The component of lift (the force of the air on the wings that is perpendicular to the wings) that is toward the center of the circle.]

When applying Newton's second law to an object in circular motion at constant speed, identify the forces or force components that are directed toward the center of the circle. Then, add these forces to get the net force, and apply Newton's second law.

These are just the highlights. You should now practice analyzing the motion of objects in circular motion at constant speed.