PHYS16 – Lecture 11

Ch. 6 Circular Motionhttp://xkcd.com

• Circular Motion – Definitions– Tangential vs. Radial– Angular position, velocity, acceleration

• Uniform circular motion –α=0– Uniform vs. Nonuniform– Centripetal Force

• Solving problems with Circular Motion

Ch. 6 Circular Motion

Circular Motion pre-question

• Tarzan is swinging across a lake on a vine that may not support his weight. What is the most likely point for the vine to break at?

A

CB

D

Circular Motion pre-question

• An object is swung in uniform circular motion vertically. Where is the tangential acceleration the greatest?

A) At the top of the circleB) At the bottom of the circleC) At the point midway between top and bottomD) At both the top and bottom of the circleE) None of the above

Circular Motion pre-question

• A pickup has a crate of apples in its bed. The pickup makes a right turn and the once stationary crate accelerates to the left with respect to the truck bed and hits the side of the pickup. In which direction is a force acting on the crate?

A) To the rightB) To the leftC) Not enough information

Uniform Circular Motion

Uniform Circular Motion

Non-uniform circularmotion – both aT and aC

http://sciencefair.math.iit.edu/projects/forces/roller_coaster.jpg

Uniform circular motion – α =0only centripetal accel. (aC)

http://www.faqs.org/photo-dict/photofiles/list/409/2271alarm_clock.jpg

Centripetal Force

• Force pointing radially inward that keeps an object going in a circular path

rmrvmmaF

rmaF

C

C

22

ˆ

Demo – Ball on String with meter/mass

Discussion Questions

• If I spin a mass in a vertical circle:– Do I apply a constant force to maintain a constant

linear speed?– Where is the string most likely to break?

• If I spin a bucket of water in a vertical circle:– Where is the most likely spot the water will fall

out?– Does the water fall out?

No, gravity too.

At the bottom.

At the top.

No, inertia.

Inertial Forces

• Centrifugal reaction – inertia of object causes it to stay along the same path until acted on by a force

http://www.physicstutorials.org/images/stories/fcntrifugalimage.png

Centrifugal Reaction

Demo: Jar and Ball

http://www.physics.umd.edu/lecdem/services/demos/demosd1/d1-43.htm

http://vimeo.com/11817500http://www.youtube.com/watch?v=iRasoZMirRc&feature=player_embedded#at=73

Solving Problems with Circular Motion

Process of solving problems

1) Read the problem carefully!2) Draw a picture (Trick – Free Body Diagram)3) Write down the given quantities

(Trick – remember Third Law)4) Write down what you should solve for5) Identify the eqns./concepts you should use

(Trick – Second Law & separate into x/y)

6) Do the math and solve

Pendulum

• A bob of mass, m, swings in an arc. At angle, θ, what is the centripetal acceleration?

mmgTac

)cos(

What is the tangential acceleration?

)sin(gaT

Conclusions

• Angular position, velocity, and acceleration– Angular displacement vs. arc length– Angular vs. linear velocity– Angular vs. linear acceleration

• Uniform circular motion –α=0– Centripetal Force

rmrvmmaF C22

trv ˆ

rrvtra ˆˆ 2

rs