PHYS16 – Lecture 23

Ch. 10 & 11 Rotation

• Angular Motion– Angular displacement, velocity, & acceleration– Constant acceleration problems

• Angular Inertia• Angular Energy– Rotational Kinetic Energy

• Angular Force & Torque• Angular Momentum & Collisions

Ch. 10 & 11 Rotation

Rotation pre-question

• You are unwinding a large spool of cable. As you pull on the cable with a constant tension and at a constant radius, what happens to α and ω? A) Both increase as the spool unwindsB) Both decrease as the spool unwindsC) α increases and ω decreasesD) α decreases and ω increasesE) α stays constant and ω increases

Rotation pre-question

• An ice skater spins with his arms extended and then pulls his arms in and spins faster. Which statement is correct?A) His kinetic energy of rotation does not change

because energy is conservedB) His kinetic energy of rotation increases because

angular velocity increasesC) His kinetic energy of rotation decreases because

rotational inertia is decreasing

Aside on Cross Product

• Cross product or Vector product – a way to multiply two vectors to get a vector

• Right-hand Rule gives directionI like to use curling hand instead…

)sin(

) , ,(

),,(),,(

122131313232

321321

ABC

ABBAABBAABBAC

BBBAAABAC

wikipedia

Angular Force and Torque

Torque

• Torque (τ) – a force that acts at a distance causing rotation

• Units = Joules = Nm• Vector quantity, direction given by right hand

rule

)sin(

rF

Fr

wikipedia

Torque and Angular Acceleration

• F=ma so the angular equivalent would be τ=Iα• Is this true?

I

rmrrmarF

rFFr

tt

)sin(

Example: Jet turbine

• The turbine of a jet engine has a moment of inertia of 25 kg∙m2. If the turbine is accelerated uniformly from rest to an angular speed of 150 rad/s in a time of 25 s, what is the torque? If the turbine is 1.0 m long, what is the force required?

r to N 150)rsin(/F

J 15025/)150)(25(/)(

/)(

0

0

0

tII

t

t

Demo: Unrolling a spool

• When you pull the cable to the left, which way does the spool go?

University of Maryland Physics Demonstration Facility

What happens to inertia of spool as unravel?What happens to ang. velocity?What happens to ang. acceleration?

Demo: Riding a tricycle

• When you pull cable to the left, which way does the trike go?

University of Maryland Physics Demonstration Facility

Angular Momentum and Collisions

Angular Momentum

• Angular momentum (L) – momentum of a rotating object

• Cross product like the dot product is a way to multiply vectors, except cross product gives vector not scalar

• Direction of cross product is given by right hand rule

IrpL

prL

)sin(

Angular Collisions

• Angular momentum is conserved if there are no external torques

• Example: Kid jumps onto spinning merry go round, Person on a spinning chair is handed a spinning bicycle wheel, ice skater in a spin…

0L

Discussion Question: Ice Skating

• In a spin, why do ice skaters decrease their angular velocity when they hold their arms out?

http://www.corbisimages.com/images/67/7760610C-6DF3-4A39-ACD6-C3CDEFF73296/PN015983.jpg

Kristi Yamaguchi

L=IωHolding arms out increases I.If L stays the same, and I increases thenω decreases.

What about Kinetic Energy?

Conclusions

• Parameters for circular motion/ rotation basically have linear equivalents– θ is related to x, ω is related to v, α is related to a– I is related to m– Krotational is related to K

– L is related to p, L=Iω=rpsin(θ)– τ is related to F, τ=Iα =rFsin(θ)

Conclusions