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Centripetal Force
What is Centripetal Force?
Centripetal acceleration is towards
the center of the circle
Centripetal Force Video
Thus far we have applied Newton’s law, F = m*a
to linear motion. Now we’ll apply it to rotational
motion
Going in circles
Bart swings the tennis ball around his head in a
circle. The ball is accelerating, what force makes
it accelerate?
The tension in the string!
Going round in circles
• Speed may be constant
• But direction is continually
changing
• Therefore velocity is continually
changing
• Hence acceleration takes place
Centripetal acceleration
toward the
center
of the circle
Centripetal Force
• Acceleration is caused by
Force (F=ma)
• Force must be in the same
direction as acceleration
• Centripetal Force acts
towards the centre of the
circle
• Centripetal force is provided
by some external force – eg
friction
Examples of Centripetal Force
• Friction
• Tension in
string
• Gravitational
pull
Why does Centripetal Force rely on
Friction?
•Centripetal Force relies on fiction to satisfy the 3rd
law of motion.
• Centripetal force is the action to the reaction of
friction.
• Centripetal force must be greater than friction
for an object to negotiate a turn. If centripetal force
is less than friction the object will veer off in a
straight line
•This is why it is important to slow down during a
sharp turn.
•Inertia will take over the car will want to move in a
line from the point at which the forces were
unbalanced
Magnitude of centripetal acceleration
• The centripetal acceleration depends on two
factors  the speed with which you take the
turn and how tight the turn is
• More acceleration is required with a higher
speed turn
• more acceleration is required with a tighter
turn smaller radius of curvature
Wide turns and tight turns
little R
big R
for the same
speed, the tighter
turn requires more
acceleration
Centripetal acceleration
• centripetal acceleration
2
v
aC =
R
• for some turns, the “safe” speed is posted
• a force is needed to produce this centripetal
acceleration
• CENTRIPETAL FORCE
• where does this force come from?
Example
• What is the tension in a string used to twirl a 0.3
kg ball at a speed of 2 m/s in a circle of 1 meter
radius?
• Force = mass x acceleration [ m  aC ]
• acceleration aC = v2 / R = (2 m/s)2/ 1 m
= 4 m/s2
• force = m aC = 0.3  4 = 1.2 N
• If the string is not strong enough to handle this
tension it will break and the ball goes off in a
straight line.
Jeff Gordon leads his race and must drive into a curve at top speed
to win it all.
The radius of the curve is 1000.0 m and the coefficient of static
friction between his tires and the pavement is 0.500. Find the
maximum speed he can have and still make the turn. His car has a
mass of 1500 kg
Negotiating a flat (level) turn
• The centripetal force is
provided by the friction
force between the road
and tires.
• this force is reduced if the
road is wet or icy
Banked Turns
31 degree bank
Velodrome
Banked turns
N
R
FCENT
• Since the road is banked
(not horizontal) the force of
the road on the box is not
vertical
• Part of the force on the box
from the road points toward
the center of the circle
• This provides the centripetal
force
• No friction is necessary to
keep the box in the circle
Silly Silo (Rotor)
Friction between
Bart and wall
wall pushing
in on Bart
Bart’s
weight
The inward wall force keeps Bart in the circle.
Friction keeps him from falling down.
Examples of Centripetal Force
Check for Understanding Questions
•
The velocity of the particle is along the __________
• The centripetal acceleration is towards the __________
• The centripetal force acting on the particle is towards the ________
• Centripetal force causes a
change in the ________________ but no
change in ________________.
The magnitude of the centripetal
acceleration is: a =______________
Newton’s law: The force on the
particle is (centripetal force)
F= m·a = ______________