Notes: Chapter 10 Circular MotionObjectives:• Distinguish between rotation and revolution

(10.1)• Describe rotational speed. (10.2)• Give examples of centripetal force. (10.3)• Describe the motion of an object if the

centripetal force acts on it ceases. (10.4)• Explain why centrifugal force is “fictitious.”

(10.5)• Describe how a simulated gravitational

acceleration can be produced

10.1 Rotation and Revolution

• Axis is a straight line around which rotation takes place.

• Rotation is when an object turns about an internal axis; to spin.

• Revolution is when an object turns about an external axis.

10.2 Rotational Speed

• Angular displacement the angle through which a point, line, or body is rotated about a specific axis in a given direction.

rs

radiuslength arcradians in angle

1 rev = 360o = 2 rad

• Rotational speed (angular speed) – number of rotations per unit of time.– Usually expressed in rad/s, rev/min (rpm), or rev/s

t

timentdisplaceme angular speedangular

• Tangential speed (linear speed) – speed of something moving along a circular path.– Expressed in m/s, cm/s, ft/s, or in/s

– Formula only works when is expressed in rad/s

rvpath cirluar of radius speedangularvelocity

10.3 Centripetal Force• An object moving in a circular path undergoes

and centripetal acceleration (ac).

– Caused by a centripetal force (Fc)—a center directed force that cause an object to move in a curved, or circular path.• Examples:

– Whirling a can on a string– Gravity between the Earth and the Sun– Friction keeping a car on the road as it travels a curve

rvaonaccelerati lcentripeta T

c

2

•Calculating centripetal force

rmvF

curvature of radiusvelocity tangentalmassforce lCentripeta

Tc

2

2

• Adding Force Vectors

Whenever you want to identify a centripetal force on a circularly moving object, it will be the net force that acts exactly toward the center of the circular path. In Figures 10.12 and 10.13, it is the x-components.

10.4 Centripetal and Centrifugal Forces• Sometimes there is an apparent

outward force attributed to circular motion.

• Called centrifugal force (means center-fleeing).

– The “centrifugal-force effect” is attributed not to any real force but to inertia—the tendency for a body to follow a straight-line path.

10.5 Centrifugal Force in a Rotating Frame of Reference

• Frame of reference for moving car and – ground– another moving car

• Forces also have frames of reference

• Ladybug in can, force feels as real as gravity, an interaction force.

• But the force on ladybug is due to circular motion.– Stop the circular motion and the force disappears.

Thus centrifugal force is not an interaction and therefore a fictitious force.

• Centrifugal force is an effect of rotation. It is not part of an interaction and therefore it cannot be a true force.