Mr. Rogers' AP Physics C: Mechanics (With IB Physics Topics) Objectives Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter Gravity Circular Motion Statics Rotation

Chapter 10: Rotation

E. Circular motion and rotation (continued) 1% (estimated), cumulative 89%
3. Rotational kinematics and dynamics
4. Angular momentum and its conservation

 Practice Test Study Guide
 Objectives
 Essential Question: How do linear phenomenon relate to rotational phenomenon?

Rotational Motion Basics

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

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

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

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

5. Indicate which rotational quantities are vectors and which are scalars.

6. 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)

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

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

9. Solve problems with rotational kinematics equations.

10. Calculate rotational kinetic energy.

Homefun: Questions 1-5 Problems 1, 3, 7. Serway

Chapter 16, The Movie Merry-Go-Round: 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)

 Activities

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 1-8. 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

1. State the Earth's rotational velocity in RPM, RPS, tangential velocity, and w.
2. Spin down time on a wheel.
3. Swinging door problem. q = 2t^3 - 3t^2 +5t + 7, Find q, w, a  @ t=10 sec.
4. Calculate the rotational kinetic energy stored in Earth in joules, megatons of TNT, and Tsar bombs.
radius = 6.371 x 106 meters,
mass = 5.9736×1024 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

1. Derive the rotational inertia for :
• a rod swinging around its end
• a rod rotating around its middle
• a disk
1. Use the parallel axis theorem.

I = Icm + mD2

1. 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

1. derive all equations in objective 11
2. use parallel axis theorem
3. 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

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

2. 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.)

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

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

5. Find the net torque on a wheel.

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

7. 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 yo-yo?

Linking the Rotational Motion to the Linear Motion

1. Solve yo-yo 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 Law--linear & rotational versions--with the linkage equation: a = ra

2. 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 3Key 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

1. Solve swinging rod problems for velocity.

2. Solve yo-yo problems (string wrapped around a disk) using conservation of energy.

3. Calculate the power required to turn a winch that raises a weight at constant velocity.

power = tw

1. 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 4Key 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

1. 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
1. Calculate the period of various pendulums.
2. 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 5Key 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

1. Solve ice skater problems.
• change in rotational velocity--conservation of angular momentum
• change in rotational kinetic energy--why is K not conserved?
1. Solve rod and blob collision problems.
2. Solve pendulum collision problems.
3. Solve planetary motion in elliptical orbits problems.

Summative Assessment : Unit Exam objectives 1- 33

 Lesson 6Key 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

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