Download Centripetal force

Centrifugal and Centripetal Force
Vectors and Direction
Key Question:
How do we describe circular motion?
Motion in Circles
• We say an object rotates
about its axis when the axis is
part of the moving object.
• A child revolves on a merrygo-round because he is
external to the merry-goround's axis.
Angular Speed
• Angular speed is the rate at which
an object rotates or revolves.
• There are two ways to measure
angular speed
– number of turns per unit of time
(rotations/minute)
– change in angle per unit of time
(deg/sec or rad/sec)
Angular Speed
• For the purpose of
angular speed, the
radian is a better unit for
angles.
• One radian is approx.
57.3 degrees.
 Radians are better for angular speed because a
radian is a ratio of two lengths.
Angular Speed
Angular speed
(rad/sec)
w=q
t
Angle turned (rad)
Time taken (sec)
Calculate angular speed
• A bicycle wheel makes six
turns in 2 seconds.
• What is its angular speed in
radians per second?
Linear and Angular Speed
• A wheel rolling along the ground has both a linear speed and an
angular speed.
• A point at the edge of a wheel moves one circumference in each turn
of the circle.
Linear and Angular Speed
Circumference
(m)
C=2Pr
Radius (m)
Distance (m)
Speed
(m/sec)
v = d2 P r
t
Time (sec)
Linear and Angular Speed
Linear speed
(m/sec)
v=wr
Radius (m)
Angular speed
(rad/sec)
*This formula is used in automobile
speedometers based on a tire's radius.
Linear and Angular Speed and
Displacement
Centripetal Force
Key Question:
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.
Centripetal Force
Mass (kg)
Centripetal
force (N)
Fc = mv2
r
Linear speed
(m/sec)
Radius of path
(m)
Calculate centripetal force
• 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?
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 = v2
r
Speed
(m/sec)
Radius of path
(m)
Calculate centripetal acceleration
• A motorcycle drives around a bend with a 50-meter radius
at 10 m/sec.
• Find the motor cycle’s centripetal acceleration and
compare it with g, the acceleration 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 called 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.