## Introductory Mechanics and Relativity

Newtonian mechanics and special relativity. Topics include vectors; kinematics in three dimensions; Newton’s laws; force, work, power; conservative forces, potential energy; momentum, collisions; rotational motion, angular momentum, torque; static equilibrium, oscillations, simple harmonic motions; gravitation, planetary motion; fluids; special relativity.

*Note: ***Principles of Scientific Inquiry (PSI)** is the laboratory component of Physics 15a. Topics include experimental design, model testing, error analysis, basic programming, oral presentations, and scientific writing. PSI will meet weekly throughout the semester. This course, when taken for a letter grade, meets the General Education requirement for Science of the Physical Universe or Empirical and Mathematical Reasoning, but not both. This course, when taken for a letter grade, meets the Core area requirement for Science A.

### Spring 2018

Week 1 Lab Safety and Introduction to PSI Lab (experiment: inclined rolling bottle)

Week 2 Central Limit Theorem and 1D data analysis (experiments: reaction time)

Week 3 Chi-square model testing I (experiment: air drag)

Week 4 Chi-square model testing II and Introduction to projects

Week 5 Project 1

Week 6 Project 1

Week 7 Project 1

Week 8 Project 2

Week 9 Project 2

Week 10 Project 2

Projects chosen by students to model and test:

1. falling coffee filters

2. inclined channel

3. swinging Atwood machine

4. gravity well

5. ball revolving around the inside of a cylinder

6. parametric pendulum

7. spherical pendulum

8. sphere on a rotating turntable

9. superball rebounding under a tabletop

### Spring 2017

Week 1 Lab Safety and Introduction to PSI Lab (experiment: inclined rolling bottle)

Week 2 Central Limit Theorem and 1D data analysis (experiments: reaction time)

Week 3 Chi-square model testing I (experiment: air drag)

Week 4 Chi-square model testing II and Introduction to projects

Week 5 Project 1

Week 6 Project 1

Week 7 Project 1

Week 8 Project 2

Week 9 Project 2

Week 10 Project 2

Projects chosen by students from the following:

1. Modeling and testing falling coffee filters

2. Modeling and testing an inclined channel

3. Modeling and testing of a swinging Atwood machine

4. Determining Fractal dimensions

5. Modeling and testing of Gauss’ gun

6. Modeling and testing amplitude growth in a parametric pendulum

7. Modeling and testing for a spherical pendulum

8. Modeling and testing a sphere on a rotating turntable

9. Modeling and testing a superball rebounding under a tabletop

### Spring 2015

Week 1 Introduction to PSI (experiment: inclined rolling bottle)

Week 2 Central Limit Theorem and 1D data analysis (experiments: coin toss; reaction time)

Week 3 Pendulum: Modeling and data collection (experiment: rigid pendula of various lengths)

Week 4 Testing and Revising the Pendulum model; Project Introduction

Week 5 Project 1

Week 6 Project 1

Week 7 Project 1

Week 8 Project 2

Week 9 Project 2

Week 10 Project 2

Projects chosen by students from the following:

1. Determining velocity dependance and drag coefficient for falling coffee filters

2. Predicting acceleration down an inclined channel

3. Modeling and testing of the Swinging Atwood machine

4. Determining Fractal dimensions

5. Modeling and testing of Gauss’ gun

6. Predicting and testing amplitude growth in a parametric pendulum

7. Predicting precessing advance for a spherical pendulum

8. Predicting angular velocity ratio (sphere/turntable) for a sphere on a rotating turntable

### Fall 2013

Week 1 Introduction to PSI with experiment

Week 2 Probability and Statistics I (experiment: reaction time)

Week 3 Probability and Statistics II (experiment: coin toss)

Week 4 Introduction to Modeling (experiment: rigid pendulum)

Week 5 Testing Assumptions (experiment: rigid pendulum)

Week 6 Project 1

Week 7 Project 1

Week 8 Project 1

Week 9 Project 2

Week 10 Project 2

Week 11 Project 2

Projects chosen by students from the following:

1. Air drag

2. Duffing oscillator

3. Falling chains

4. Fractal dimension

5. Gauss gun

6. Parametric pendulum

7. Rocker oscillator

8. Rolling sphere on turntable

9. Zeeman oscillator

10. Inverted pendulum

11. Rotating disk and gravity

### Spring 2013

Week 1 Introduction to PSI with experiment

Week 2 One‐variable data analysis (experiment: reaction time)

Probability and Statistics (experiment: coin toss)

Week 3 Exploratory Data Analysis: (experiment: unforced pendulum)

Week 4 Two-variable data analysis (experiment: unforced pendulum [group data]

Week 5 Two‐variable data analysis (experiments: unforced pendulum [class data] and phase plane analysis)

Week 6 Project 1

Week 7 Project 1

Week 8 Project 1

Week 9 Project 2

Week 10 Project 2

Week 11 Project 2

Projects chosen by students from the following:

1. Air drag

2. Coefficient of restitution

3. Duffing oscillator

4. Falling chains

5. Fractal dimension

6. Gauss gun

7. Parametric pendulum

8. Rocker oscillator

9. Rolling sphere on turntable

10. Zeeman oscillator

### Fall 2012

Week 1 Introduction to Scientific Inquiry

Week 2 Experiment #1: Elevator

Week 3 Analysis #1: Probability & Statistics

Week 4 Analysis #2: Probability & Statistics

Week 5 Experiment #2: Pendulum

Week 6 Analysis #3: Examining Assumptions

Week 7 Final Projects

Week 8 Final Projects

Week 9 Final Projects

Final projects chosen by students from the following:

1. Elevator-turned-pendulum.

Why does it start to swing? What’s the significance of the magic frequency?

How does the swinging amplitude grow with time?

2. Driven oscillator.

How does the oscillation amplitude grow with time?

3. Kinetic friction.

Is the traditional model for kinetic friction good? Does the kinetic friction force depend on contact area? velocity?

4. Drag forces in liquid.

How does the drag force on a sphere depend on velocity? size? properties of the fluid?

5. Drag forces in air.

How does the drag force on falling coffee filters depend on

velocity? size? properties of air?

6. Gauss gun.

Why does the ejected ball come out so fast? Does this violate conservation of

momentum? What about energy?

7. “Diver” in water column.

What explains the strange behavior of the diver? Where is the equilibrium position? Is it stable or unstable? Why?

8. Chain drop.

How fast does the chain fall? What’s the normal force during the drop? What about lifting the chain off the plate?

9. Rubber band oscillator.

Does a stretched rubber band obey Hooke’s Law? What’s the frequency of the cart’s oscillation if you attach the rubber bands to the ends of the cart? What if you attach them to the sides?

### Spring 2008

- Lab #1: Measurement and Uncertainty: Pendulum Period
- Lab #2: Gauss Gun: Conservation of Momentum; Work and Energy
- Lab #3: Force Plate: The Vertical Jump
- Lab #4: Harmonic Oscillations and Damping

### Spring 2007

- Lab #1: Speed of Sound