Transcript Aim: How can we explain circular motion?

Aim: How can we explain
circular motion?
Do Now:
An object travels 5 m/s north
and then travels 5 m/s east.
Has the object accelerated?
Velocity is defined by two things:
•Magnitude (5 m/s)
•Direction (north)
Direction has changed
Therefore velocity has changed
A change in velocity is defined as acceleration
Up to now, we only dealt with linear acceleration
(objects traveling in a straight line speeding up or
slowing down)
Changing direction – this is centripetal acceleration
In what direction does velocity act?
Demo
 Velocity acts tangent to the
circle made by the object.
v
v
v
v
In what direction does
acceleration act?
 Acceleration acts
inward, towards the
center.
Is there a force?
 Yes
 Newton’s 2nd law – unbalanced forces
produce acceleration
 If there is acceleration, there must be
an unbalanced force
 This is centripetal force
In what direction does the
force act?
The force acts inward, towards the
center.
Centripetal force and
the centripetal
acceleration are always
pointing in the same
direction
Fc
Fc
Fc
Fc
Centripetal force is not
a separate force
It is whatever force is
pointing towards the
center of the circle
In this example, the
normal force is pointing
towards the center of
the circle
Therefore the normal
force is the centripetal
force
What is supplying the centripetal force?
Spinning an object attached to a string in a circle
Tension in the string
Turning a car
Friction between the tires and the road
Ever drive and hit a patch of ice?
No more friction -- no more turn
The car skids in a straight line (tangent to the circle)
Walking in a circle
Friction between your shoes and the floor
Ever try to run in dress shoes and make a sharp turn?
OUCH!
If centripetal
force is directed
towards the
center, why do
you feel a
“force” pushing
you away from
the center of the
circle when in
this motion, like
turning in a car?
The object gets pushed
away from the center
Remember velocity?
The object wants
remain in motion
tangent to the circle
The car just gets in the
way
This gives the “illusion”
of a force that really
does not exist!
Water in cup Demo
(during lab)
How can we calculate
centripetal acceleration?
2
v
ac 
r
 Where v is the velocity and r is the
radius of the circle traveled by the
object
How do we calculate the
centripetal force?
F = ma, so Fc = mac
Substitute in ac =v2/r
2
mv
Fc 
r
A car whose mass is 500 kg is traveling around
a circular track with a radius of 200 m at a
constant velocity of 15 m/s.
What is the centripetal acceleration?
Given
m = 500 kg
r = 200 m
v = 15 m/s
a
acc ==1.1
? m/s2
Fc = ?
v2
ac 
r
What is the
centripetal force?
(15 m / s) 2 Fc = mac
ac 
200 m
Fc = (500 kg)(1.1 m/s2)
ac  1.1 m / s
2
Fc = 550 N
What if the velocity isn’t
given?
 The distance traveled by the
object is the circumference of
the circle; C = 2πr
r
d 2r
v 
t
t
Example
A 615 kg racing car completes one lap in 14.3 s around a
circular track with a radius of 50.0 m. The car moves at
a constant speed.
(a) What is the acceleration of the car?
Given
m = 615 kg
d = c = 2πr
t = 14.3 s
r = 50 m
ac =?
v2
ac 
r
d 
 
t

ac 
r
 2 (50 m) 


14.3 s 

ac 
50 m
2
 2r 


t 
ac  
r
2
(22 m / s) 2
ac 
50 m
2
ac  9.7 m / s 2
(a)What force must the track exert on the tires
to produce this acceleration?
Given
m = 615 kg
d = c = 2πr
Fc = mac
t = 14.3 s
Fc = (615 kg)(9.7 m/s2)
r = 50 m
Fc = 5,965.5 N
ac = 9.7 m/s2
Fc = ?