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16.6 Uniform Circular Motion and Simple Harmonic Motion

- The pendulum's displacement is a function of time.

- The motion of the pendulum is a function of time.

- The ruler has a higher force for the same amount of displacement.
- It hurts more when the ruler snaps your hand.

- You are observing something.
- One way you could decrease the system's maximum speed is to identify it.

- You can increase the mass of the object.

- There is an easy way to produce simple motion.
- The shadow of a ball is projected on the floor by a rotating vertical turntable.
- Hooke's law doesn't usually describe systems with large visible displacements.
- Simple motion produced in this manner can give a lot of insight into many aspects of waves and oscillations.
- Some of the major features of this relationship will be indicated in our brief treatment.

- The shadow of a ball on a turntable goes back and forth in a simple motion.

- The figure shows the relationship between the two motions.
- The point P is traveling around the circle.
- The object on the merry-go-round is similar to the point P. The projection of the position of P onto a fixed axis is similar to the shadow of an object.
- The projection moves to the left at the time shown in the figure.
- The point P around the circle is equal to the point on the - axis.

- A point P is moving on a circular path.
- The point around the circle and its projection are shown.

- The velocities form a triangle similar to the displacement triangle.

- The time for one revolution is when the radians are at their highest.

- We can use Figure 16.19 to do some further analysis of uniform circular motion.

- It is possible to get all of the characteristics of simple motion from an analysis of the projection.

- Let's take a look at the period of the projection.
- The point P is needed to complete one revolution.
- The time is divided by the speed around the circle.

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