Run

A ball travels in a circle of radius 4.0 m, the center of the circle is marked with a red dot. The ball starts at rest and increases its speed steadily. The green vector shows the velocity of the ball and the blue vector shows the acceleration. Time is in seconds and positions are in meters.

The table below the animation gives the speed of the ball, the angle between the acceleration and the velocity, and the components of acceleration. (Because of the way the angle is computed, it may read positive or negative, and may be an equivalent angle: i.e. -30° or 330°.

• Initially what is the angle between a and v?
• After a long time, what does the angle between a and v approach?
• Pause the animation and calculate the radial (centripetal) acceleration by using v²/r.
• Advance the animation a small time and calculate the tangential acceleration by using Δv/Δt.
• From the values of the tangent and radial components of acceleration, can you determine the angle between v and a? Why does this work?