• Lecture 1. units
  • 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?
  • 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,  i with hat on top comma space j with hat on top comma space k with hat on top.
      • 2. Describe the position of a point that is located at an angle  30 degree from the horizontal, and has a length of 2 m, using conventional static unit vectors,  i with hat on top comma space j with hat on top comma space k with hat on top.
    • II. Coordinate System Nomenclature
      • 1. If  stack e subscript 1 with overbrace on top equals i with hat on top comma space stack e subscript 3 with hat on top equals j with hat on top comma space stack e subscript 3 with hat on top equals k with hat on top, rewrite question 1 in part 1, using the  e with overbrace on top base vectors.
      • 2. If  stack e subscript 1 with overbrace on topmakes an angle of  30 degreewith the horizontal, rewrite question 2 in part 1 using the  e with hat on top base vectors.
    • III. Derivative of position (one-dimensional)
      • If r with rightwards harpoon with barb upwards on top equals open parentheses 3 space m over s close parentheses space cos open parentheses open parentheses 5 space fraction numerator r a d over denominator s end fraction close parentheses t close parentheses space i with hat on top, what are  v with rightwards harpoon with barb upwards on top and  a with rightwards harpoon with barb upwards on top?
      • If null. what are  v with rightwards harpoon with barb upwards on top and  a with rightwards harpoon with barb upwards on top?
      • If  r with rightwards harpoon with barb upwards on top equals space open parentheses negative 3 space m over s squared close parentheses space t squared space j with hat on top, what are  v with rightwards harpoon with barb upwards on top and  a with rightwards harpoon with barb upwards on top?
    • 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,  g space equals space 9.8 space m over s, 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 x open parentheses t close parentheses equals sin space open parentheses t close parentheses, what is  fraction numerator d x over denominator d t end fraction?
      • If  y open parentheses t close parentheses equals 2, what is  fraction numerator d y over denominator d t end fraction?
      • Evaluate  a with rightwards harpoon with barb upwards on top equals space fraction numerator d over denominator d t end fraction open parentheses fraction numerator d x over denominator d t end fraction i with hat on top plus fraction numerator d y over denominator d t end fraction j with hat on top close parentheses
    • 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  t subscript f
      • 7. For the values,  h space equals space 10 space m,  stack v subscript 0 with rightwards harpoon with barb upwards on top equals 2 space m over s i with hat on top plus 4 space m over s j with hat on top (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, t subscript f.
      • 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