PHYS16 – Lecture 11
http://xkcd.com
Ch. 6 Circular Motion
Ch. 6 Circular Motion
• 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
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?
D
A
B
C
Circular Motion pre-question
• An object is swung in uniform circular motion
vertically. Where is the tangential acceleration
the greatest?
A)
B)
C)
D)
E)
At the top of the circle
At the bottom of the circle
At the point midway between top and bottom
At both the top and bottom of the circle
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 right
B) To the left
C) Not enough information
Uniform Circular Motion
Uniform Circular Motion
Non-uniform circular
motion – both aT and aC
http://sciencefair.math.iit.edu/projects/forces/roller_coaster.jpg
Uniform circular motion – α =0
only 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

F  maC rˆ
F  maC  m v r  m r
2
2
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
No, gravity too.
linear speed?
– Where is the string most likely to break? At the bottom.
• If I spin a bucket of water in a vertical circle:
– Where is the most likely spot the water will fall
At the top.
out?
– Does the water fall out?
No, inertia.
Inertial Forces
• Centrifugal reaction – inertia of object causes
it to stay along the same path until acted on
by a force
Centrifugal Reaction
http://www.physicstutorials.org/images/stories/fcntrifugalimage.png
Demo: Jar and Ball
http://www.physics.umd.edu/lecdem/services/demos/demosd1/d1-43.htm
http://vimeo.com/11817500
http://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 for
5) 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?
T  mg cos( )
ac 
m
What is the tangential acceleration?
aT   g sin(  )
Conclusions
• Angular position, velocity, and acceleration
– Angular displacement vs. arc length
s  r

– Angular vs. linear velocity
v  rtˆ

• Uniform circular motion –α=0
– Centripetal Force
F  maC  m v r  m r
2


a  rtˆ  v 2 r rˆ
– Angular vs. linear acceleration
2