Circular Motion

Chapter 9

Objectives:Distinguish between rotate and revolve.Describe rotational speed.Give examples of centripetal force.Describe motion of an object if the centripetal force acting on it ceases.Explain why centrifugal force is ‘fictitous’.Describe how a simulated gravitational acceleration can be produced.

Look at Fig 9.1 pg 122Why do the occupants of this carnival ride not fall out when it is tipped almost vertical?

Which moves faster on a merry-go-round, a horse near the outside rail or one on the inside rail?

Axis- the straight line around which rotation takes place.

Rotation-when an object turns about an internal axis (located within the body of the object) Also called spin.

Revolution- when an object turns about an external axis. Also referred as revolve about its axis

Key terms:AXIS, ROTATION, REVOLUTION

Axis- the straight line around which rotation takes place.

Rotation-when an object turns about an internal axis (located within the body of the object) Also called spin.

Revolution- when an object turns about an external axis. Also referred as revolve about its axis

Key terms:AXIS, ROTATION, REVOLUTION

Does a tossed football rotate or revolve?

Does a ball whirled overhead at the end of a string rotate or revolve? Rotate or

Revolve?

What are other examples?

Linear speed- distance moved per unit of time (remember Ch.2)

Tangential speed- the speed of something moving on a circular path.

For circular motion, we can use the above terms interchangeably.

Rotational speed- number of rotations per unit of time. (sometimes called angular speed)

All parts of the RIGID merry-go-round rotate about their axis in the same amount of time, thus all parts have the same rate of rotation.

Key terms:Linear speed, tangential speed, rotational speed

Have you heard of RPM’s??

Rotational speed means the same number of rotations per unit of time.

Linear speed is the distance per unit of time while rotational speed if the number of rotations per unit of time.

Linear speed varies with the distance from the axis of rotation.

Therefore…if in a circle linear speed is interchangeable with tangential speed we can say the following…

Linear speed is NOT the same as rotational speed.

Tangential speed is directly proportional to the radial distance from the axis of rotation and the rotational speed

V=rw (w is the Greek letter omega)

Period, Frequency, and Speed

Period: the time it takes for one full rotation or revolution of an object.

T =1/fThis is a measure of time so the SI unit is second.

Frequency: the number of rotations or revolutions per unit of time.

f = 1/TThe unit is called a hertz(Hz)

Speed (while traveling in a circle) speed = 2

Activity on page 126Rolling on Tapered Wheels

Centripetal force-any force that causes an object to follow a circular path.

Means ‘center-seeking’This is not a new force; it is ANY force

that is directed at a right angle to the path of a moving object and tends to produce a circular motion.

Key term:Centripetal Force

Examples of centripetal forceGravitational force directed toward the center of the Earth holds the moon in an almost circular orbit

Electrons revolving around the nucleus of an atom.

A Centrifuge…what is a washing machine?

Simulated Gravity

• True Gravitational force is always an interaction between one mass and another. The gravity we feel is due to the interaction of our mass and the mass of Earth.

• Gravity is simulated by centrifugal force.

• In a rotating reference frame the centrifugal force has no agent such as mass……there is no interaction therefore it cannot be a TRUE force.

• Centrifugal force is an effect of rotation. That’s why it is referred as fictitious.

Centripetal Acceleration An object can move around in a circle with a constant speed yet still be accelerating because its direction is constantly changing. This acceleration is always directed in toward the center of the circle.The magnitude of this acceleration is written

Centripetal acceleration (ac) = (linear speed)2

radius

Centripetal ForceIf an mass is being accelerated toward the center of a circle, it must be acted upon by an unbalanced force that gives it this acceleration. This Force is always directed inward toward the center of the circle.The magnitude of this force is written

Centripetal force (Fc) = mac = mv2 r