Circular Motion

Vocabulary for Circular Motion

Period(T): the time it takes for one rotation or revolution. Measured in seconds.

Revolution: traveling about an external axis, kid on merry-go-round

Rotation: spinning about an internal axis, an ice skater spinning

Centripetal force: a center-seeking force, causes circular motion

Two types of speed to think about:

Linear Speed is total distance divided by time. In circular motion, total distance is equal to circumference or 2πr. The time is equal to the period.

Rotational speed (AKA angular speed) refers to the number of rotations/revolutions per unit of time. A common unit for this is RPM. Any guesses on what RPM stands for?

Linear Speed

With linear speed, a point on the outer edge of an object moves a greater distance in one rotation than a point closer to the center of the object.

Two ladybugs sit on a rotating disk, as shown in the figure (the ladybugs are at rest with respect to the surface of the disk and do not slip). Ladybug 1 is halfway between ladybug 2 and the axis of rotation. A) Which has a great linear speed? B) Which has a greater rotational speed?

Speed/Velocity in a CircleConsider an object moving in a circle around a specific origin. The DISTANCE the object covers in ONE REVOLUTION is called the CIRCUMFERENCE. The TIME that it takes to cover this distance is called the PERIOD.

T

rv

2

Speed is the MAGNITUDE of the velocity. And while the speed may be constant, the VELOCITY is NOT. Since velocity is a vector with BOTH magnitude AND direction, we see that the direction, and thus, the velocity, is ALWAYS changing.

We call this velocity, TANGENTIAL velocity as its direction is drawn TANGENT to the circle.

CENTRIPETAL FORCE

centripetal force- a center directed force that causes an object to move in a curved (sometimes circular) path. Centripetal means "center-seeking" or "toward the center".

It is any force that is at a right angle to the path of a moving object that has a circular motion.

As you can see by this picture, when on a roller coaster that has a loop, the passengers experience centripetal force, as well as inertia.Centripetal force can be found with the following equations:

Fc = ma= mv2/r= m4π2r/T2

ANALYZING THE FORCES

http://library.thinkquest.org/27948/carousel.html

Centripetal or Centrifugal Force ???Centripetal and Centrifugal Forces

centrifugal force- an apparent outward force on a rotating or revolving body. It is fictitious. Due to the fact that our velocity is constantly tangent to the circular path we are following, a force has to constantly be pushing/pulling us toward the center. The pressure we feel as a result of the inward force tricks our minds into thinking we are being pushed outward.

Video for reviewCentrigal Force- NOT http://www.youtube.com/watch?v=Sav9vQ663u4

Centripetal AccelerationIf an object moves in a circle it is accelerating and there has to be an unbalanced force acting on it. A force that causes circular motion is always toward the center. Acceleration is always in the same direction as the force (so centripetal acceleration is toward the center). If, for instance, you tie a weight on a string and swing it around over your head in a circle you can feel the centripetal force needed to keep it going in a circle. If you let go, that is remove the centripetal force, it will fly off in a straight line in whatever direction it happens to be going at that moment. Centripetal acceleration is found using the following equations:

ac= v2/r= 4π2r/T2

Drawing the Directions correctly

So for an object traveling in a counter-clockwise path. The velocity would be drawn TANGENT to the circle and the acceleration would be drawn TOWARDS the CENTER.

To find the MAGNITUDES of each we have:

r

va

T

rv cc

22

In what direction will the car continue if the curve he is about to travel around is solid ice starting from point B?

In what direction will the car continue if the curve he is about to travel around is solid ice starting half way between point B and C?

A .013-kg ball is attached to a 0.93-m string. The ball is swung in a horizontal circle, making one revolution in 1.18 s. Find the tension force exerted by the string on the ball.

What is the direction of the force that acts on clothes in the washing machine in the spin cycle?

What is the name and direction of the force on the ball below?What is the name and direction of the acceleration?

Label as Rotating(x) or Revolving(y)A. Earth traveling around the sun

B. Moon traveling around the earthC. Earth spinning D. Kid on seesawE. Person on roller coaster traveling around a loopF. Dog chasing his tailG. Ice Skater SpinningH. A doorI. Discus thrower (in reference to the person)J. Discus thrower (in reference to the disk)

Book Assignment:Page 172-173, 49-54