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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
