Download Dan Burns Calculus Approach

Dan Burns show details Jun 22 (9 days ago) Reply
to AP
I do Mech. C only. I think you will have to go into more detail in E&M but
not much. I will use the terms "dot product" and "scalar product" and point
out resources in their physics book for additional information. I don't
emphasize the rote mathematical formula, abcos(phi). Instead I talk about
determining the component of the force in the direction of motion to
calculate the work done. I show how a force applied perpendicular to the
direction of motion can't change the kinetic energy so no work can be done
by it. I don't say that the dot product is always a cosine. We show how to
determine the component of the force in the direction of motion using
whatever angles are given in the problem. I intentionally give them problems
where the angle is given so that a sine is used.
I don't go into details about the cross product either. The full treatment
is only needed for 3D problems which are not treated in my class. We show
that torque is only produced by the component of force perpendicular to the
lever arm. This is easy to demonstrate by poking the door handle in a
direction parallel to it. We say that torque is the component of force
perpendicular to the lever arm times the lever arm. I also show the other
way to think about it, torque is the force times the component of the lever
arm perpendicular to the force. I don't emphasize absin(phi) or do any
matrices. I give them problems here the angle is given so that a cosine
might be used.
I treat the angular momentum of a particle in a similar way. A particle only
has angular momentum if it has a component of velocity perpendicular to the
lever arm. This can be demonstrated by shooting a projectile parallel to a
rotating platform. When it hits, the platform will not rotate. Angular
momentum is the only place where we talk about the direction of a vector
that is the cross product of 2 other vectors. I sit on a chair that can spin
freely with a spinning bicycle wheel with the plane of rotation parallel to
the ground. When I flip it, L has to keep the same direction. That means I
will have to start spinning in the direction the wheel was spinning before I
flipped it. It helps to have a wheel with a large I for this demo. We use
the right hand rule to predict which way I will spin given the wheel's
direction and to determine which way the wheel was spinning after seeing
which way I spun. We also use the RHR to determine the direction of L for
various spinning systems diagrammed on the board.
Dan Burns
Los Gatos High School
(where students need a pencil, a calculator, and a right hand for the
rotation test)