main circular motion

8/8/2019 Main Circular Motion

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Concept Summary


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Circular Motion Terms

The point or line that is the centerof the

circle is the axis of rotation.

If the axis of rotation is inside theobject, the object is rotating

(spinning).

If the axis of rotation is outside theobject, the object is revolving.


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Linear/Tangential Velocity

Objects moving in a circle still have a

linear velocity = distance/time.

This is often called tangential velocity,since the direction of the linear velocity

is tangent to the circle.v


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Rotational/Angular Velocity

Objects moving in a circle also have arotationalorangular velocity, which isthe rate angular position changes.

Rotational velocity is measured indegrees/second, rotations/minute (rpm),etc.

Common symbol, [ (Greek letteromega)


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Rotational/Angular Velocity

Rotational velocity =Change in angle

time


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Rotational & Linear Velocity

If an object is rotating:

All points on the object have the same

rotational (angular) velocity. All points on the object do nothave the

same linear (tangential) velocity.


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Linear velocity of a point depends on:

The rotational velocityof the point.

More rotational velocity means more linearvelocity.

The distance from the point to the axis of

rotation.

More distance from the axis means more linearvelocity.


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In symbols:

v = r[

v

r [


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Acceleration

As an object moves around a circle, its

direction of motion is constantly

changing. Therefore its velocity is changing.

Therefore an object moving in a circle is

constantly accelerating.


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Centripetal Acceleration

The acceleration of an object moving in

a circle points towardthe center ofthe circle.

This is called a centripetal (center

pointing) acceleration.

a


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Centripetal Acceleration

The centripetal acceleration depends

on:

The speed of the object. The radius of the circle.

Acent =

v2

r


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Centripetal Force

Newtons Second Law says that if an

object is accelerating, there must be a

net force on it. For an object moving in a circle, this is

called the centripetal force.

The centripetal force points towardthe centerof the circle.


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Centripetal Force

In order to make an object revolve

about an axis, the net force on the

object must pull it towardthe centerof the circle.

This force is called a centripetal(center

seeking) force.Fnet


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Centripetal Force

Centripetal force on an object depends

on:

The objects mass - more mass meansmore force.

The objects speed- more speed means

more force.

And


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Centripetal Force

The centripetal force on an object alsodepends on:

The objects distance from the axis(radius). Iflinear velocityis held constant, more

distance requires less force.

Ifrotational velocityis held constant, more

distance requires more force.


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Centripetal Force

In symbols:

Fcent=mv2r

= mr[2


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Work Done by the Centripetal

Force

Since the centripetal force on an object

is always perpendicular to the objects

velocity, the centripetal force neverdoes work on the object - no energy is

transformed.

v

Fcent


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Centrifugal Force

Centrifugal force is a fictitious force -

it is not an interaction between 2

objects, and therefore nota realforce.

Nothingpulls an object away from

the center of the circle.


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Centrifugal Force

What is erroneously attributed to

centrifugal force is actually the action

of the objects inertia-

whatevervelocity it has (speed + direction) it

wants to keep.


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The End

main circular motion

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