Download Chapter 10 – Simple Harmonic Motion

Chapter 5
Uniform Circular Motion
Chapter 5 Objectives (*vocab)
1. Centripetal Acceleration
centripetal*
uniform circular motion*
period*
formula for ac
2. Centripetal Force
centrifugal*
3. Banked Curves
4. Satellites & Apparent Weight
artificial gravity*
5.1 Uniform Circular Motion (U.C.M.)
Conditions for U.C.M.
Constant circular speed
Velocity is always changing and tangent to the path.
Acceleration is towards the center of the circle.
5.1 Uniform Circular Motion (U.C.M.)

Circumference (C)

Diameter (d)
C

d
  3.14159...
C d
C  2 r
5.1 Uniform Circular Motion (U.C.M.)
Period (T) – time required to travel one revolution
distance 2 r
v=

time
T
5.2 Centripetal Acceleration (ac)
An object in U.C.M. is always accelerating b/c
the direction is always changing.
ac = centripetal accleration
Centripetal means ‘center-seeking’
2
v
ac 
r
5.2 Centripetal Force (Fc)
Centripetal Force – any force directed toward
the center of a circle. ‘center-seeking’
The centripetal force
keeps an object
moving in a circular
path; without this
force, the object
would fly off tangent
to the path.
Examples of Centripetal Force
Friction
Tension
Gravity
REMEMBER: Centripetal force is NOT a new type of force;
it is just any force that keeps an object in circular motion.
Centrifugal Force – fictitious force arising from
circular motion and inertia. “center-fleeing’
Motion in a Vertical Circle
Example : A ball is spinning in a vertical circle at the end of a
string that is 2.0m long. If the ball has a mass of 3.5kg and
moves at a constant speed of 8.0m/s…
a) Calculate the centripetal force that keeps the ball from
flying away. Does this force change as the ball moves
around the circle?
112N, this force remains constant
b) What two forces contribute to the centripetal force at the
top of the circle? Calculate their values.
Weight = 34 N, Tension = 78N
c) What two forces contribute to the centripetal force at the
bottom of the circle? Calculate their values.
Weight = 34 N, Tension = 146 N
Water will ‘flee’ out of the bucket if the bottom of
the bucket did not provide a centripetal force.
In this case, water will ‘flee’ out of the hole in
the bucket because of an absence of a
centripetal force, NOT because of a centrifugal
force.
Objects inside the car will ‘flee’ from the circular
path because of INERTIA and the absence of a
centripetal (center-seeking) force NOT because
of a outward force.
Centrifugal Force is NOT a real force!
It is due to inertia and circular motion.
Concept Check:
True or False:
1. An object moving in circular motion at a constant speed
is accelerating.
True
2. If an object is moving in circular motion, there must
be a centripetal force acting on the object at all times. True
3. As a car rounds a corner at a constant speed, the
car is accelerating.
4. Without a centripetal force, an object can not move
in circular motion.
True
True
5. As an object moves in circular motion, a centrifugal
force will always push objects away from the center. False
A ball is swung in circular motion as shown.
6. Draw the direction of the velocity vector.
7. Draw the direction of the acceleration vector.
a
v
Homework #1:
Ch. 5 #1, 2, 3, 6, 8
p. 148
Homework #2:
Ch. 5 #13, 15, 18
p. 148
5.4 Banked Curves
When a car rounds a banked curve, the
normal force of the road supplies a
centripetal force
5.4 Banked Curves
Fc = FNsinθ
PRACTICE:
Ch. 5 #12-22 (evens only)
p. 148
v1 – v2 is NOT zero, even though v1 = v2
These triangles are similar
v r

v
r
as t  0, r  vt
v vt

v
r
v v

t r
2
ac  v
2
r
ac = centripetal accleration
v
ac 
2
r