16.6 Uniform Circular Motion and Simple Harmonic Motion

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.