Notes from Five Easy Lessons

Vectors

Student vector knowledge is usually desperately lacking and it's vital for the kinematics part of physics, so spend some time working on it.

• Ensure they practice using vectors as displacements
• Practice identifying components for vectors at random locations in all four quadrants of the coordinate plane
• Add, subract, and scale vectors both graphically and with coordinate ops
• Work within tilted coordinate systems
• Emphasize proper use of significant-figures
• Require proper vector notation in all cases - it's important to solidify the difference between vectors and scalars, especially for things like dot product that involve both.
• Review the main trigonometric ratios (sin,cos,tan) and practice relating them to vector components
• Find the angle of a vector
• Find the parallel and perpendicular decomp of a vector with respect to a tilted line (specify the angle of the line sometimes, and the slope other times).

Motion and Kinematics

Intuitive understanding of motion is almost always both wrong and deeply entrenched. It takes extra time to untangle beliefs and get the mind thinking in terms of position, acceleration, and velocity.

• Start with a picture of a ramp that shows a ball in various positions (separated equally in time not space) as it accelerates down the ramp
• Ask them to identify the average velocity of the ball over each gap
• Ask them to identify the acceleration of the ball
• Most students confuse velocity and acceleration
  • "positive" acceleration doesn't mean "speeding up", it means the acceleration vector is pointing in the positive direction
  • Consider why the acceleration vector in centripetal acceleration has to point toward the center of the circle
• Use a motion-diagram to illustrate the true situation
• Let them practice relating graphs of motion properties
  • graph position, velocity, and acceleration
  • Figure out what the missing graph should look like based on the provided one(s)
  • Connect concepts with motion diagrams to help understand how graping one thing is graphing the rate of change at any given time for another
  • Focus on understanding how it looks when we put time on the horizontal axis and position on the vertical (especially when the actual position is changing in the horizontal direction!) This is very confusing when you first see it.