CENTRIPETAL FORCE

Centripetal Force is the force required to change the direction of a moving object.

Newton’s 1st Law version 2.0:An object at rest stays at rest and an object in motion stays in straight line motion unless acted upon by a net force.

CENTRIPETAL FORCE

So how do we get something to "turn"?

We apply a force like this:

Perpendicular to the direction of motion

CENTRIPETAL FORCE

We talk about a “Force”. Recall that where there is a net force, there is ____________

CENTRIPETAL FORCE

We talk about a “Force”. Recall that where there is a net force, there is Acceleration.

CENTRIPETAL FORCE

Imagine a ball being spun around in a horizontal circle at a fixed speed: 2.00 m/s.

Where is the acceleration? The speed is fixed?

CENTRIPETAL FORCE

Velocity is a vector:

It has speed and direction.

If we change speed, we accelerate.

If we change direction, we must, by definition, accelerate as well !

CENTRIPETAL FORCE

Let’s examine how this works:

Above is our definition of acceleration. There is no numerical difference, so we need to use vectors to find the directional difference

CENTRIPETAL FORCE

From the previous page we draw the velocity vectors:

v1

v2

We will subtract them vectorially and find the difference…the difference will be v, our numerator in a = v/t

CENTRIPETAL FORCE

First we have to create a negative v …

v1

CENTRIPETAL FORCE

First we have to create a negative v …

v1 -v1

CENTRIPETAL FORCE

Then we ‘add’ them:

-v1

v2

CENTRIPETAL FORCE

Then we ‘add’ them:

-v1

v2

CENTRIPETAL FORCE

Then we ‘add’ them:

-v1

v2v2-v1 = v

CENTRIPETAL FORCE

More importantly, look at the direction of the accelerated motion…

It’s pointed directly at the center!

CENTRIPETAL FORCE

CENTRIPETAL: from Latin centrum "center" and petere "to seek"

CENTRIPETAL FORCE

Derivation of centripetal acceleration equation:

CENTRIPETAL FORCE

Derivation of centripetal acceleration equation:

-v1

v2v2-v1 = v

CENTRIPETAL FORCE

Derivation of centripetal acceleration equation:

-v1

v2v2-v1 = v

CENTRIPETAL FORCE

Derivation of centripetal acceleration equation:

-v1

v2v2-v1 = v

r

CENTRIPETAL FORCE

Derivation of centripetal acceleration equation:

-v1

v2v2-v1 = v

r

r

CENTRIPETAL FORCE

Derivation of centripetal acceleration equation:

-v1

v2v2-v1 = v

r

r

x

CENTRIPETAL FORCE

r r

x

Derivation of centripetal acceleration equation:

-v1 v2

v2-v1 = v

r

r

x

CENTRIPETAL FORCE

r r

x

-v1 v2

v

CENTRIPETAL FORCE

r r

x

-v1 v2

v

x v

R v

CENTRIPETAL FORCE

x v

R vxv

vR

Now put this in our equation for acceleration:

va

t

CENTRIPETAL FORCE

va

txvRat

CENTRIPETAL FORCE

va

txvRat

xva

Rt

CENTRIPETAL FORCE

va

txvRat

xva

Rtv x

aR t

CENTRIPETAL FORCE

va

txvRat

xva

Rtv x

aR t

vv

R

CENTRIPETAL FORCE

So finally we get:

2va

r CENTRIPETAL

ACCELERATION

2vF m

r

CENTRIPETAL FORCE