1. PHYS16 – Lecture 23
Ch. 10 & 11 Rotation

2. Ch. 10 & 11 Rotation Angular Motion Angular Inertia Angular Energy
Angular displacement, velocity, & acceleration
Constant acceleration problems
Angular Inertia
Angular Energy
Rotational Kinetic Energy
Angular Force & Torque
Angular Momentum & Collisions

3. 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?
Both increase as the spool unwinds
Both decrease as the spool unwinds
α increases and ω decreases
α decreases and ω increases
α stays constant and ω increases

4. Rotation pre-question
An ice skater spins with his arms extended and then pulls his arms in and spins faster. Which statement is correct?
His kinetic energy of rotation does not change because energy is conserved
His kinetic energy of rotation increases because angular velocity increases
His kinetic energy of rotation decreases because rotational inertia is decreasing

5. Aside on Cross Product
Cross product or Vector product – a way to multiply two vectors to get a vector
Right-hand Rule gives direction
I like to use curling hand instead…
wikipedia

6. Angular Force and Torque

7. Torque Torque (τ) – a force that acts at a distance causing rotation
Units = Joules = Nm
Vector quantity, direction given by right hand rule
wikipedia

8. Torque and Angular Acceleration
F=ma so the angular equivalent would be τ=Iα
Is this true?

9. 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?

10. Demo: Unrolling a spool
When you pull the cable to the left, which way does the spool go?
What happens to inertia of spool as unravel?
What happens to ang. velocity?
What happens to ang. acceleration?
University of Maryland Physics Demonstration Facility

11. Demo: Riding a tricycle
When you pull cable to the left, which way does the trike go?
University of Maryland Physics Demonstration Facility

12. Angular Momentum and Collisions

13. 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

14. 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…

15. Discussion Question: Ice Skating
In a spin, why do ice skaters decrease their angular velocity when they hold their arms out?
Kristi Yamaguchi
L=Iω
Holding arms out increases I.
If L stays the same,
and I increases then
ω decreases.
What about Kinetic Energy?

16. 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)

17. Conclusions