Uniform Circular Motion

- For now, our circular motion problems will be constant

speed problems. (that’s the uniform part.)

- An object experiencing uniform circular motion is not

experiencing constant velocity. (Why not?!)

- An object experiencing uniform circular motion is

experiencing constant acceleration. (Why?!)

- A period (T) is time, but a particular time. It is the time

for one complete rotation or revolution (of an object in

circular motion.) (Also used for oscillations.)

- What is the distance an object moving in a circle travels

in one complete circle? Given the radius, how can you

find this distance?

- Average speed = that distance / period =

This is a “special case” equation. Don’t forget the

conditions for it to be true.

Centrifugal vs. Centripetal

- Any object traveling in a circle (or any curved path

though we will only deal with circular paths) is

experiencing a centripetal acceleration.

- The word centripetal means “center-seeking”.

The direction of centripetal acceleration is towards the

center of curvature (of the circular path.)

The direction of a_c is perpendicular to the velocity.

Thus, a_c CAN NOT (and does not) change the speed!

- Since there is some acceleration, there MUST BE a non-

zero net force. This is the centripetal force.

It must be (and is) in the same direction as the a_c.

- Centrifugal (center-fleeing) Force is the word we use for

the sensation we feel but it is only the reaction force to

the “real” centripetal force causing the acceleration.

(Note: centrifuge.)

Centripetal acceleration = v² / r

where v is the speed and r the radius of curvature.

Note units for centripetal acceleration:

Centripetal Force

Note that centripetal force is never a separate free body diagram force. It is the NET force that is causing the centripetal acceleration that results in the circular motion of the object. Its source must always be identified in order to solve the problems.

- For a kid sitting on the floor of a merry-go-round

F_c =

- For a car on a banked curved road

F_c =

- For a person in a rotating round room at the carnival

F_c =

- For a ball swung about in a circle on a string

F_c =

- For a planet or satellite in orbit

F_c =

- For a car going around a corner on a flat curve

F_c =

- For a car cresting the top of a hill

F_c =

Weightlessness in Space Flight

Remember the person standing on a scale in an elevator problem.

- As they accelerate upwards, they feel ___________

- As they accelerate downwards, they feel __________

- What if the cable breaks and they freefall?

A state of freefall is equivalent to a state of weightlessness.

Is there no gravity is this scenario? Clearly there is gravity.

What about astronauts aboard the orbiting space shuttle?

- Isaac Newton’s thought experiment…

- Being in orbit is being in a state of freefall.

- There is plenty of gravity. There has to be.

Otherwise, the spacecraft wouldn’t stay in orbit.

- At the altitude of the space station,

g is still nearly 9.0 m/s/s. (8.8 m/s/s)

Artificial Gravity

Al Einstein’s Principle of Equivalence

- Being in a gravitational field is equivalent to being

in an accelerated reference frame.

- No experiment can distinguish the difference.

Consequences:

- Light, which is massless, will be deflected by a

gravitational field.

- Space must be curved and gravity is the cause.

(Einstein’s General Theory of Relativity.)

- An accelerating frame of reference can provide an

artificial gravitation field for (future) space travelers.