- Lecture 1. units
- I. The lecture on units (part one). The SI system of units and notes
- What agreement defines the SI systems of units?
- What is the date of the latest agreement?
- What are the important mechanical base units?
- What law defines the derived unit, the newton?

- II. The lecture on units (part two). naming, abbreviations, exponents, and prefixes
- Example 1. exponents and prefixes
- What is the correct way to write the name of the unit named after Sir Isaac Newton? What is the correct abbreviation for this unit?
- What is the correct way to write the name of the unit named after Michael Faraday? What is the correct abbreviation for this unit?
- If you were to have a unit named after you, what would you want this unit to be called (write it correctly)? What would you want the abbreviation to be?
- Write using a prefix.
- Write using a prefix.
- Write Mg using a prefix (mega-grams).
- Write pm using a prefix (pico-meters).

- III. The lecture on units (part three). derived units
- Example 2. convert from basic to derived
- Multiply and leave the answer in an appropriate derived unit. .

- IV. The lecture on units (part four). US Customary units
- Example 3. US Customary to SI
- What empire provides the origin for US Customary units?
- Is the United States officially metric?
- What is a remnant of the 1970s push for adoption of the metric system? Look around and see if you can find a remnant other than mine. If possible, take a picture.
- Unit Conversion Examples – Notes

- I. The lecture on units (part one). The SI system of units and notes
- Lecture 2. gravitation
- I. Newton’s Laws [video]
- If an unbalanced force that points to the right is acting on a particle, what direction does the particle accelerate?
- If a particle is moving to the left at 1 m/s and an unbalanced force that points to the right acts on the particle, what happens to the velocity? (a. increases to the left, b. decreases to the left, c. stays the same, d. flips to the right)
- If one particle exerts a force of 1 N acting to the left on another particle, what is the force that the second particle exerts on the first?

- II. Newton’s Law of Gravitation [video]
- What is the value of the universal gravitation constant (include units)?
- What is the force exerted by two 1 kg masses separated by 1 m?

- III. Acceleration due to gravity [video]
- Mass of earth is 5.972 × 10^24 kg.
- Mass of mars is 6.39 × 10^23 kg.
- Radius of earth (average) is 6378 km.
- Radius of mars (average) is 3,390 km.
- Using Earth’s geoid [https://rechneronline.de/earth-radius/] to find the radius of Earth for latitude, 45 degrees, and longitude, 22 degrees, what is the value of acceleration due to gravity at that location?
- What is the acceleration due to gravity for a mass that is 1 km above the surface of the earth at that latitude and longitude?
- What is the approximate acceleration due to gravity on earth at average radius?
- What is the acceleration due to gravity on Mars?

- I. Newton’s Laws [video]
- Lecture 3. Straight line motion
- Straight line notes [PDF]
- 1. Description of a point
- 1. Describe the position of a point that is located 4 m in the x direction, 2 m in the y direction, and 3 m in the z direction, using conventional static unit vectors, .
- 2. Describe the position of a point that is located at an angle from the horizontal, and has a length of 2 m, using conventional static unit vectors, .

- II. Coordinate System Nomenclature
- 1. If , rewrite question 1 in part 1, using the base vectors.
- 2. If makes an angle of with the horizontal, rewrite question 2 in part 1 using the base vectors.

- III. Derivative of position (one-dimensional)
- If , what are and ?
- If null. what are and ?
- If , what are and ?

- IV. Aside
- There are no questions for this part.

- V. A mass accelerating under gravity (dropping)
- 1. A 1 kg mass is dropping in a uniform gravity field, , from an initial height, 10 m. How long does the mass take to hit the ground? What velocity is the mass travelling when it hits the ground?
- 2. A 2 kg mass is dropping in a uniform gravity field. If the mass takes 1 s to hit the ground, how high was it initially? What is the velocity of the mass when it hits the ground?

- VI. Curvilinear Motion (2D)
- If , what is ?
- If , what is ?
- Evaluate

- VII. Projectile Motion
- 1. What is the vector differential equation for projectile motion?
- 2. What are the two scalar differential equations for projectile motion?
- 3. What are the equations for x and y for projectile motion?
- 4. What are the equations for x and y velocity for project motion?
- 5. What is the equation for range?
- 6. Solve the quadratic equation to get an expression for
- 7. For the values, , (initial velocity in x and y), what is the range, R, for a 1 kg projectile?
- 8. For the projectile in 7, what is the time when the projectile hits the ground, .
- 9. For the projectile in 7, what is the y component of the velocity as a function of time?

- Lecture 4. Matrices
- Lecture 5. Coordinate Transformation
- Lecture 6. Angular Velocity
- Lecture 7. Velocity and Acceleration Formulas
- Lecture 8. Straight line dynamics
- Lecture 9. Planar rigid body motion and Moment of inertia
- Lecture 10. Planetary Gear System
- Lecture 11. Using Python to Solve dynamics problems

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