Centrifugal and Centripetal Force

Vectors and DirectionKey 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 merry-go-round because he is external to the merry-go-round'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

= t

Angle turned (rad)

Time taken (sec)

Angular speed (rad/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

C = 2 r

Radius (m)Circumference

(m)

v = d t

Distance (m)Speed(m/sec)

Time (sec)

2 r

Linear and Angular Speed

v = rRadius (m)

Linear speed(m/sec)

Angular speed(rad/sec)

*This formula is used in automobile speedometers based on a tire's radius.

Linear and Angular Speed and Displacement

Centripetal ForceKey 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

Fc = mv2

r

Linear speed(m/sec)

Radius of path(m)

Centripetalforce (N)

Mass (kg)

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

ac = v2

r

Speed(m/sec)

Radius of path(m)

Centripetalacceleration (m/sec2)

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

• 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.

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.

Centrifugal Force

• 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.

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.