

Essential Question:
How do linear phenomenon
relate to rotational phenomenon? 
Rotational Motion Basics

State the rotational equivalents of the linear
quantities mass (p. 301, see table 10.2 on p.304), velocity, acceleration, and force (p.306).

State the 2 types of vector multiplication and
describe the differences between them.

For rotational inertia or moment of inertia,
state the dominate effect, distance from the center of rotation or mass.

Convert between various methods of expressing
rotational velocities. ω, RPS, RPM

Indicate which rotational quantities are vectors
and which are scalars.

Use the right hand thumb rule to represent
rotational vectors as arrows where the length is proportional to the magnitude
and the arrow head represents the direction. (Figure 10.3, p. 295)

By looking at the arrows representing rotational
velocity and acceleration, determine if an object's rotation is speeding up or
slowing down.

By looking at the arrows representing rotational
acceleration determine the direction of the arrow representing the torque
vector.

Solve problems with rotational kinematics
equations.

Calculate rotational kinetic energy.
Homefun: Questions 15 Problems 1, 3, 7. Serway

Read:
Insultingly Stupid Movie Physics
 Chapter 16, The Movie MerryGoRound: How
Filmmakers Create Ridiculous Spin, pp 273  287
Metacognition Problem Solving Question
10.1:
What type of problem is this (energy, momentum, kinematics,
etc) and how can I take the linear motion equation and translate it into a
rotational form? For every linear motion equation and principle there
is a rotational counterpart. In other words if you know the equations and
principles of motion in the linear world you know them in the rotational world.
(See the Rotational Study Guide)



Lesson 1
Key Concept:
Every quantity and equation in the linear world has a counterpart in
the rotational world.
Purpose:
Enable students to write rotational equations, given linear
equations addressing similar situations.
Interactive Discussion:
Objective 18. List the linear and their corresponding rotational
quantities on the board.
Demo 10.1:
Objective 1, 400 grams of mass taped on the end of a meter stick.
Have students balance the mass on their hand first with the mass
close to the hand and second with the mass as far as possible from
the hand. Which way is easier and why?
In Class Problem Solving:
Objectives 9 and 10
 State the Earth's rotational velocity in RPM,
RPS, tangential velocity, and w.
 Spin down time on a wheel.
 Swinging door problem. q
= 2t^3  3t^2 +5t + 7, Find q, w, a
@ t=10 sec.
 Calculate the rotational kinetic energy stored
in Earth in joules, megatons of TNT, and Tsar bombs.

radius =
6.371 x
10^{6} meters,
 mass = 5.9736×10^{24}
kg,
 1
megaton TNT = 4.18 E13
 1 Tsar Bomb = 100
megatons
Resources/Materials: Meter
stick, tape, and 2, 200 gram weights. 

Essential Question:
How does the shape of an
object and the axis of rotation affect its rotational inertia? 
Rotational or Moment of
Inertia
 Derive the rotational inertia for :
 a rod swinging around its end
 a rod rotating around its middle
 a disk
 Use the parallel axis theorem.
I = I_{cm} + mD^{2}
 Calculate rotational inertias by adding the inertias
for the parts of an object.

Lesson 2
Key Concept:
Rotational inertia.
Purpose: derive
moment of inertia for various geometries.
Demo 10.2:
Simultaneously roll a hoop and a disk down an incline. Observe which
one gets there first?
 Interactive Discussion:
Objective s
In Class Problem Solving at boards:
Objectives
 derive all equations in objective
11
 use parallel axis theorem
 calculate the rotational inertia of a mace

Essential Question: How does the rotational
motion of an engine get transformed into linear motion of a car? 
Linking the Rotational Motion to the Linear
Motion

State the three key equations which link the linear and rotational worlds.

Calculate the acceleration of the free end of a
rod which rotates around a fixed pivot on one end as it falls. (See example
10.10, p.309.)

Given a wheel's w solve for its linear velocity and vice versa.

Given a wheel's a solve for its linear acceleration and vice versa.

Find the net torque on a wheel.

Use the rotational version of Newton's second
law. (See example 10.9, p.307.)

Calculate the max torque which can be exerted on
a wheel without making it spin.
Max Torque = (mg)mR
Relevance: Max torque that can be exerted on a wheel without making it spin is a key design feature in all wheeled vehicles.
Metacognition Problem Solving Question
10.2: Is the problem a mixture of rotational and linear motion in which I can write
equations for both types of motion and if so, how can I relate rotational motion
to linear motion? There is an equation which links the linear world to the rotational world for
every property of motion in physics. These are shown below:

1) 
v 
= 
rw 

2) 
a 
= 
ra 

3) 
x 
= 
q r 

4) 
t 
= 
(F) x (r) 
Homefun (formative/summative assessment): prob. 33, 35, 37, 59


Lesson 3
Key Concept: There are three key equations which link the linear and rotational worlds.
Purpose: Show
how rotation and linear motion interact.
 Interactive Discussion: Objective
In Class Problem Solving: Objectives
 See objectives 13 to 21


Essential Question:
How can you calculate the accelerations of a yoyo? 
Linking the Rotational Motion to the Linear
Motion

Solve yoyo problems.
a disk (note, a cylinder is an elongated disk) with a string wrapped around it for several turns and creating a single tension force acting on the pulley.
the tension force is in the string is created by a falling object
to solve use Newton's 2nd Lawlinear & rotational versionswith the linkage equation: a = ra
 Solve pulley problems. (See example 10.12,
p.310.)
a disk with a string wrapped around it for less that one turn, creating a tension force on each side of the pulley.
Formative assessment): In class guided practice,
Homefun (formative/summative assessment): selected problems. 

Lesson 3 Key Concept:
There are three key equations which link the linear and rotational worlds.
Purpose: Show
how rotation and linear motion interact.
 Interactive Discussion:
Objective
In Class Problem Solving:
Objectives
 See objectives 13 to 21


Essential Question:
Which is easier solving
rotational problems with energy equations or Newton's 2nd law? 
Rotational Kinetic Energy

Solve swinging rod problems for velocity.

Solve yoyo problems (string wrapped around a
disk) using conservation of
energy.

Calculate the power required to turn a winch that
raises a weight at constant velocity.
power =
t∙w

Solve belt problems. Relevance:
Belt drives are ubiquitous on various types of mechanical equipment, for example
the belt on a car's engine that drives the car's alternator, power steering,
power brakes, air conditioner, etc.
Homefun
(formative/summative assessment): prob. 45, 47


Lesson 4 Key Concept:
Rotational Work, Power, and Energy
Purpose: Apply
conservation of energy to rotational problems
 Interactive Discussion:
Objectives 22 to 25
In Class Problem Solving:
Objectives 22 to 25
 See objectives 22 to 25


Essential Question:
How can the period be
calculated of any type of pendulum? 
Pendulums
 Derive the equation for the period of a generic
pendulum.
T = 2 π
(I / mgd)^{0.5}
 Where:
 I = moment of inertia
 m = mass
 d = distance from pivot
point to center of mass
 Calculate the period of various pendulums.
 Derive the equation for the period of a torsional pendulum.
T = 2 π
(I / κ)^{0.5}
 Where:
κ
=
torsional spring constant

=
t
/ q
Homefun
(formative/summative assessment):
prob.

Lesson 5 Key Concept:
derivation of pendulum equations
Purpose: Apply
conservation of energy to rotational problems
 Interactive Discussion:
Objectives
In Class Problem Solving:
Objectives
 See objectives


Essential Question:
Why does an ice skater
spin faster when she pulls in her arms? 
Rotational Momentum
 Solve ice skater problems.
 change in rotational velocityconservation of
angular momentum
 change in rotational kinetic energywhy is K not
conserved?
 Solve rod and blob collision problems.
 Solve pendulum collision problems.
 Solve planetary motion in elliptical orbits problems.
Summative Assessment :
Unit Exam objectives 1 33

Lesson 6 Key Concept:
rotational momentum
Purpose: Apply
conservation of momentum to rotational problems.
Demo 10.3:
Spin a student in a swivel chair while holding dumb bells. Pull the
dumb bells in and out. Observe the changes in rotation.
Demo 10.4:
Have a student sit in a swivel chair while holding a spinning
bicycle wheel. Turn it vertically and horizontally. Observe the
changes in rotation.
 Interactive Discussion:
Objectives
In Class Problem Solving:
Objectives


