Chapter 7.3 Notes
7:3 Periodic and Circular Motion
This is motion of objects as they travel in a circle; twirling a rock on the end of a string, a car going around a race track, riding a Ferris Wheel, the earth orbiting the sun......
There are two types of uniform circular motion:
Lets use the example of twirling a rubber stopper in a horizontal (level) circle on the end of a string.
Note then, that a centripetal force is necessary to keep an object accelerating centripetally. Can you think of any possible uses for this in space?
Lets take a look at how it applies to keeping a car going around a flat, circular course.
This section deals with motion in which the force varies directly with displacement; such as Hook's Law
F = kx, where F is the applied force, k is a constant of proportionality (dependent on the configuration of the system), and x is the distance the object moves. Other examples are a pendulum, a child on a swing, a guitar string, a spring....etc.
The period, T, of a pendulum is , where l is the length of the string (or more precisely, as measured from the center of mass of the system) , and g is the acceleration due to gravity. A pendulum is used to measure the gravity at
different locations; this is an important tool in the search for minerals.
Check this website out: A Pendulum Clock
Rotary motion is the motion of a body about an internal axis. Examples are a spinning bicycle wheel, the spinning crankshaft of a car, and a cheerleader doing a cartwheel.
In the previous chapters we expressed linear displacement in terms of mm, cm, m, and km.
In this section we define angular displacement , (theta), the measure of the angle in which the object moves through. The units of angular displacement are revolutions, degrees, and radians. Angular velocity, (omega), is the time rate of angular displacement or .
Angular acceleration , (alpha), is the rate of change of angular velocity or .
, or, which for rotary motion is analogous to F = ma for linear motion.
For linear motion, inertia is equal to the mass of the object. For rotary motion, inertia must take into account both shape and mass; therefore different shapes have different rotational inertia.
Homework: set #4 Ch 7 questions 10-14 page 170
Set #5 Ch 7 problems 49-55, page 172-173