Forces and Circular Motion
Sources:
v
ar
r
Since there is a radial acceleration,
there must be a net radial force
Fnet,r = mar = mv2/r
called Centripetal Force
But what about Centrifugal Force?
NOT A REAL FORCE !!
-Objects want to travel in a straight line, and resist
being pulled in a circle.
-Outward force “felt” by an object is a result of
trying to work in an accelerating reference frame.
REMEMBER: NEWTON’S LAWS ONLY WORK IN
NON-ACCELERATING REFERENCE FRAMES!
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Friction
Tension
Normal forces
Gravity
Example: ball on a string in horizontal circular motion.
Fix r and double v. How does T change?
Demos
Q1,2
2
T = mv2/r
T∝ v
If T>Tmax, the string will break.
rTmax
vmax =
m
Example: Conical Pendulum
Find:
1. ar
ar = v2/(Lsinθ
θ)
2. θ
Tcosθ
θ
L
Recall: for circular motion,
ar = v2/r
Centripetal Forces
m
θ
Tsinθ
θ
mg
θ
T
v
ΣFy = Tcosθ – mg = 0
ΣFx = Tsinθ = mar = mv2/(Lsinθ)
1
Car on icy horizontal curve
Car on a Banked Ramp
y
Given: m = 1500 kg
R= 35.0 m
µs = 0.500 dry; 0.050 icy
what is vmax for no slipping?
N
θ
ar Nsinθ
x
ΣFx = Nsinθ = max
= mv2/R
ΣFy = Ncosθ - mg
= may = 0
ΣFx = fs = mv2/R
ΣFy = N - mg = 0
θ
Ncosθ
θ
θ
N
N = mg
fs,max = µsN = µsmg
v max = Rµ s g
mg
fs
mg
What if you consider
static friction?
N = mg/cosθ
(mg/cosθ) sinθ = mv2/R
tan θ = v2/(Rg)
2