Unit 2C: Circular Motion

Centripetal force keeps an object in circular motion.

Which moves faster on a carousel, a horse near the outside rail or one near the inside rail?

We begin by first discussing the difference between rotation and revolution.

axis:

line around which rotation takes place

• rotation: (spinning)

object turns about an internal axis(axis within object’s

body)

• revolution: (circling)

object turns about an external axis

9.1 Rotation and Revolution

A Ferris wheel rotates (spins) about an axis (at the center).

Each riderrevolves (circles) about its axis.

9.1 Rotation and Revolution

axis

Earth undergoes both types of rotational motion.

• It revolves (orbits) around the sun once every 365 ¼ days.

• It rotates around its own axis through its poles once every 24 hours.

9.1 Rotation and Revolution

(1 year)

(1 day)

The record rotates around its axis while the bug sitting at its edge revolves around the same axis.

9.2 Rotational Speed

Which part moves faster—the outer part where the ladybug sits or a part near the orange center?

It depends: do you mean linear or rotational speed?

linear velocity:

distance traveled per unit of time

• A point on the edge travels further in one rotation than a point near the center, so…

• linear speed is greater on the edge of a rotating object than it is closer to the axis.

tangential velocity: (linear)

speed of object moving along a circular path

(the direction is always tangent to the circle)

9.2 Rotational Speed

rotational velocity: (angular velocity)

number of rotations per unit of time

• All parts of the record have the same rate of rotation, or the same number of rotations per unit of time.

• commonly express rotational velocity in revolutions per minute (RPM).

9.2 Rotational Speed

9.2 Rotational SpeedAll parts of the record rotate at the same rpm.

a. A point further from the center travels a longer path in the same time and therefore has a greater tangential velocity.

All parts of the record rotate at the same rpm.

a. A point further from the center travels a longer path in the same time and therefore has a greater tangential velocity.

b. A ladybug sitting twice as far from the center moves twice as fast.

9.2 Rotational Speed

Tangential and Angular Velocity

Tangential velocity is directly proportional to the angular velocity and the radial distance from the axis of rotation.

9.2 Rotational Speed

tangential velocity ~ radial distance × angular velocity

proportional

radial distance: (radius)

distance from the center axis of rotation

v ~ r

think!At a playground, you and a friend stand on a merry-go-round. You stand at the edge and have a rotational velocity of 4 RPM and a linear velocity of 6 m/s. Your friend stands halfway to the center.

What is his rotational velocity?

What is his linear velocity?

His rotational velocity is 4 RPM (same), but …

his linear velocity is 3 m/s (half as much)

9.2 Rotational Speed

Railroad Train Wheels

How do the wheels of a train stay on the tracks?

The train wheels stay on the tracks because their rims are slightly tapered.

9.2 Rotational Speed

A curved path occurs when a tapered cup rolls. The wider part of the cup travels a greater distance per revolution.

A tapered cup rolls in a curve because the wide part of the cup rolls faster than the narrow part.

Fasten a pair of cups together at their wide ends and roll the pair along a pair of parallel tracks.

• The cups will remain on the track.• They will center themselves whenever they

roll off center.

9.2 Rotational Speed

The wheels of trains are similarly tapered. This shape is essential on the curves of railroad tracks.

• On any curve, the distance along the outer part is longer than the distance along the inner part.

• The outer wheels travel faster than inner wheels.

9.2 Rotational Speed

When a train rounds a curve, the wheels have different linear velocities for the same angular velocity.

9.2 Rotational Speed

1. Rotation takes place about an axis that is internal. Revolution takes place about an axis that is…

A. outside the object.

B. at the center of gravity.

C. at the center of mass.

D. inside the object.

Quick Quiz!

2. When you roll a tapered cup across a table, the path of the cup curves because the wider end rolls …

A. slower.

B. at the same speed as the narrow part.

C. faster.

D. in an unexplained way.

Quick Quiz.

When the can moves in a circle at a constant speed, does it accelerate?

• speed is constant but direction changes so velocity changes (acceleration).

• change in direction must be due to a net force (or the can would continue to go in a straight line).

9.3 Centripetal Force

Yes!

centripetal force:inward force directed

toward the center causing any object to have a circular path

What applies this force?

Centripetal force is not a basic force of nature, but is the name given to any force that is directed toward a fixed center.

Centripetal force is exerted in different ways:

• gravitational forces hold planets and moons in orbit.

• electrical forces act between an orbiting electron and the atomic nucleus in an atom.

• friction force keeps a car on a curved path.

• tension force in a rope keeps a tethered ball in a circle around a pole.

9.3 Centripetal Force

Anything that moves in a circular path is acted on by a centripetal force perpendicular (at a right angle) to the object’s path.

9.3 Centripetal Force

9.3 Centripetal Forcea. For a car to go around a curve, there must be

enough friction to provide the required centripetal force to change its direction.

a. For a car to go around a curve, there must be enough friction to provide the required centripetal force to change its direction.

b. If the force of friction is not great enough, skidding occurs as the car’s inertia keeps it going in a straight line.

9.3 Centripetal Force

The clothes in a washing machine are forced into a circular path, but the water is not, and it flies off in a straight line tangent to the circle.

9.3 Centripetal Force

Video Clipsof Circular Motion

http://www.teachersdomain.org/resource/psu10phy.sci.centripetal/

http://www.teachersdomain.org/resource/lsps07.sci.phys.maf.circmotion/

http://www.teachersdomain.org/resource/phy03.sci.phys.mfw.roller/

http://safari4.volusia.k12.fl.us/SAFARI/montage/playlistedit.php?SearchType=my&Action=MakeActive&playlistkeyindex=12563&location=local

Sometimes it seems like there’s an outward force caused by circular motion.

9.4 Centripetal and Centrifugal Forces

centrifugal force:outward “force” directed away from the

center of a circular path

It’s a common misconception to state that a centrifugal force pulls outward on the can, BUT…when the string breaks the can goes off in a tangent straight-line path because no force acts on it.

So when you swing an object around, there is actually no force pulling it outward.

9.4 Centripetal and Centrifugal Forces

When the string breaks (centripetal force stops) the object’s inertia keeps it moving in a straight line, tangent to—not outward from the center of—its circular path.

9.4 Centripetal and Centrifugal Forces

Neglecting gravity, the only force exerted on the bug is the force of the can on its feet. (centripetal)

From our outside stationary frame of reference, we see there is no centrifugal force exerted on the bug.

The can presses against the bug’s feet and provides the centripetal force that holds it in a circular path.

The ladybug in turn presses against the floor of the can.

1. When you whirl a can in a horizontal circle overhead, the force that holds the can in the path acts …

A. in an inward direction.

B. in an outward direction.

C. in either an inward or outward direction.

D. parallel to the force of gravity.

Quick Quiz!

2. Anything that moves in a circular path must be acted on by a centripetal force that is _______________ the object’s path.

A. in the same direction as

B. in the opposite direction of

C.parallel to

D.perpendicular to

Quick Quiz.

3. When you whirl a can in a horizontal circle overhead, the force that the can exerts on the string acts …

A. in an inward direction.

B. in an outward direction.

C. in either an inward or outward direction.

D. parallel to the force of gravity.

Quick Quiz.

9.4 Centripetal and Centrifugal Forces

Neglecting gravity, the only force exerted on the bug is the force of the can on its feet. (centripetal)

From our outside stationary frame of reference, we see there is no centrifugal force exerted on the bug.

The can presses against the bug’s feet and provides the centripetal force that holds it in a circular path.

The ladybug in turn presses against the floor of the can.

from the frame of reference of the ladybug inside the whirling can, the ladybug is being held to the bottom of the can by a force that is directed away from the center of circular motion.

9.5 Centrifugal Force in a Rotating Reference Frame

BUT…

From a stationary frame of reference outside the whirling can, we see there is no centrifugal force acting on the ladybug inside the whirling can.

We do see centripetal force acting on the can, producing circular motion.

9.5 Centrifugal Force in a Rotating Reference Frame

In the rotating frame of reference of the whirling can, both centripetal force and centrifugal force act on the ladybug.

centripetal force centrifugal force

9.5 Centrifugal Force in a Rotating Reference Frame

centripetal force centrifugal force

9.5 Centrifugal Force in a Rotating Reference Frame

centripetal force

centrifugal force

The centrifugal force appears to be a force as real as the pull of gravity, BUT…

there is a difference between the gravity-like centrifugal force and actual gravitational force.

Gravitational force is always an interaction between two masses. The gravity we feel is due to the interaction between our mass and the mass of Earth.

9.5 Centrifugal Force in a Rotating Reference Frame

centripetal force

centrifugal force

feels like “gravity”

The centrifugal force is an effect of rotation, but it is not part of an interaction and is not a true force.

For this reason, physicists refer to centrifugal force as a fictitious force.

But to observers in a rotating system, centrifugal force is very real. Just as gravity is ever present at Earth’s surface, centrifugal force is ever present within a rotating system.

9.5 Centrifugal Force in a Rotating Reference Frame

centripetal force

centrifugal force

feels like “gravity”

http://www.teachersdomain.org/resource/

phy03.sci.phys.mfw.roller/

ROLLER COASTER

9.6 Simulated Gravity

9.6 Simulated Gravity

http://www.youtube.com/watch?v=H9fe_4QB7Uk&safety_mode=true&persist_safety_mode=1&

safe=active

SIMULATED GRAVITY

think!Which observer sees the ball being pulled outward, stretching the spring?

Which sees thespring pulling theball into circularmotion?

9.5 Centrifugal Force in a Rotating Reference Frame

From inside the rotating reference frame, centrifugal force pulls outward on the ball, stretching the spring.

From the rest frame, only centripetal force from the stretched spring pulls the ball into circular motion.

1. A bug inside a can whirled in a circle feels a force of the can on its feet. This force acts…

A. in an inward direction.

B. in an outward direction.

C. in either an inward or outward direction.

D. parallel to the force of gravity.

Quick Quiz!

2. Imagine a rotating (spinning) space station designed to simulate gravity. If the radius of the station was ______, then it would have to spin _______ to simulate the same gravity.

A. larger, faster

B. larger, slower

C. smaller, faster

D. smaller, slower

Quick Quiz.

3. You weigh slightly less at Earth’s equator equator than at either pole. Why?

Quick Quiz.

v ~ rω

v ~ rω

v ~ rω

1 rev per day

more centrifugal

“force”