Circular Motion Uniform and Non-Uniform
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Circular MotionUniform and Non-Uniform
ReviewEquations for Motion Along One
Dimension
dt
dx
t
xv
t
xv
t
ave
0lim
dt
dv
t
va
t
va
t
ave
0lim
ReviewMotion Equations for Constant
Acceleration
•1.
•2.
•3.
•4.
atvv 0
221
00 attvxx
20vv
vave
xavv 220
2
ReviewAcceleration in Uniform Circular
Motion
Velocity is always tangent to the pathAcceleration is always perpendicular
to velocityAcceleration is center seeking
(Centripetal)
R
va
2
Review3 Laws of MotionIf in Equilibrium
If not in equilibriumChange in Motion is Due to Force
Force causes a change in acceleration!
0F
maF
Acceleration on a Curve
0t
0v
2t
2v
0a
r
va
2
2a
Acceleration on a Curve
0t
0v
2t
2v
0a
Car is always accelerating
There must be a force acting on the car!
r
va
2
Force on a Curve
Centripetal Force
0t
0v
2t
2v
0a
r
va
amF2
r
vmF
2
0F
Note: On Centrifugal ForceThere is no such thing as
centrifugal forceIt is merely the action reaction
pair of centripetal force.
Centrifugal Force
Centrifugal force you feel in a turning car is just a result of your inertia trying to maintain a straight line of motion.
Example: Car on a curveA 1,500 kg car is rounding a
curve with radius 35.0 m. If the coefficient of friction is 0.500 find the maximum speed the car can have without slipping.
Example: Car on a curveMax velocity is related to max
acceleration is related to Centripetal force
No slipping means Centripetal Force= Force of
frictionr
vmF
2
Nf
Example: Car on a curve
smv
v
grv
m
mgrv
mgr
vm
Nr
vm
1.13
)80.9)(500.0)(0.35(
2
2
2
Example: Car on a banked curveA civil engineer wishes to design
a curved ramp in such a way that a car will not have to rely on friction to round the curve without skidding (in case of rain or ice). This is done by banking the curve (tilted towards one side). If the speed of the ramp is supposed to be 13.4 m/s, and the radius is 50.0m at what angle should the curve be banked?
Example: Car on a banked curve
Example: Car on a banked curve
r
vmNF
2
sin
cos
cos
mgN
mgN
Example: Car on a banked curve
1.20)50)(8.9(
4.13tantan
tan
tan
tan
21
21
2
2
2
gr
v
gr
v
r
vg
r
vmmg
Giancoli 5-22A 1200 kg car rounds a curve of
radius 67m banked at 12o. If the car is travelling at 95 kph will a friction force be required? If so, how much and in what direction?
Vertical Uniform Circular Motion
A passenger on a Ferris wheel weighs 750N. The wheel has a radius of 100 m and moves at constant speed of 10.5m/s. Find the apparent weight of the passenger at the top and at the bottom of the wheel.
Vertical Uniform Circular Motion
At top At BottommaF
)(2
2
2
r
vgmN
r
vmmgN
r
vmwNF
)(2
2
2
r
vgmN
r
vmmgN
r
vmwNF
Non- Uniform Circular MotionRadial acceleration – causes
change in directionTangential acceleration – causes
change in speed
Artificial Gravity
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