Transcript Centripetal Force

Objective

Describe and calculate centripetal forces and
accelerations.
Centripetal Force
Why does a roller coaster stay on a track upside
down on a loop?
Centripetal Force
 We usually think of acceleration as a change
in speed.
 Because velocity includes both speed and
direction, acceleration can also be a change in
the direction of motion.
Centripetal Force
 Any force that causes an object to move in a
circle is called a centripetal force.
 A centripetal force is always perpendicular to
an object’s motion, toward the center of the
circle.
Calculating centripetal force
 The magnitude of the centripetal force needed to
move an object in a circle depends on the
object’s mass and speed, and on the radius of
the circle.
Centripetal Force
Mass (kg)
Centripetal
force (N)
Fc = mv2
r
Linear speed
(m/sec)
Radius of path
(m)
Calculating centripetal force
1.
A 50-kilogram passenger on an amusement
park ride stands with his back against the wall
of a cylindrical room with radius of 3 m. What
is the centripetal force of the wall pressing into
his back when the room spins and he is
moving at 6 m/sec?
You are asked to find the centripetal force.
2.
You are given the radius, mass, and linear speed.
3.
Use: Fc = mv2 ÷ r
4.
Solve: Fc = (50 kg)(6 m/s)2 ÷ (3 m) = 600 N
Centripetal Acceleration
 Acceleration is the rate at which an object’s
velocity changes as the result of a force.
 Centripetal acceleration is the acceleration of
an object moving in a circle due to the
centripetal force.
Centripetal Acceleration
Centripetal
acceleration (m/sec2)
ac = v 2
r
Speed
(m/sec)
Radius of path
(m)
Calculating centripetal acceleration
A motorcycle drives around a bend with a 50meter radius at 10 m/sec. Find the motor
cycle’s centripetal acceleration and compare
it with g, the acceleration of gravity.
1.
2.
3.
4.
5.
You are asked for centripetal acceleration and a
comparison with g (9.8 m/s2).
You are given the linear speed and radius of the motion.
Use: ac = v2 ÷ r
4. Solve: ac = (10 m/s)2 ÷ (50 m) = 2 m/s2
The centripetal acceleration is about 20%, or 1/5 that of
gravity.
Centrifugal Force
 We call an object’s tendency to
resist a change in its motion its
inertia.
 An object moving in a circle is
constantly changing its direction
of motion.
 Although the centripetal force pushes you toward the
center of the circular path...it seems as if there also is a
force pushing you to the outside.
 This “apparent” outward force is often incorrectly
identified as centrifugal force.
Centrifugal Force
 Centrifugal force is not a true
force exerted on your body.
 It is simply your tendency to
move in a straight line due to
inertia.
 This is easy to observe by twirling a small object at the
end of a string.
 When the string is released, the object flies off in a
straight line tangent to the circle.
v = 2π
t
v=ωr
ω=θ
t
θ=s
r
Fc = mv²
r
Fc = m ac
Centripetal Acceleration
ac = v²
r
ac = (rω)²
r
ac = r ω²