Q: I have trouble figuring out what force is nonzero and what force is zero. Additionally, I would like to clarify how the forces are negative or positive when an object is speeding up or slowing down — how do these factors influence the forces? I assume that forces like friction and weight are negative since they slow the object down, and that normal force is positive. Is this thinking correct?
A: If the question asks the Net force, it depends on the Acceleration since Acceleration is proportional to Net force due to Newton’s 2nd law. For other forces, you can usually find if zero or non-zero from the text of a problem. For example, if the object doesn’t have contact with the surface, the normal force is Zero. If the surface is frictionless, the friction force is Zero.
For non-zero forces, to tell if the force (1-D) or a component of the force (2-D) is positive or negative, generally you need to compare with the common sign conventions. Specifically, in x-axis: the Right is positive and the Left is negative, while in y-axis: the Upward is positive and the Downward is negative.
In a case of speed-up or slow-down motions, you can use the direction of velocity (motion) to find the direction of acceleration. Speed-up means Velocity and Acceleration are in a same direction. Slow-down means Velocity and Acceleration are opposite in direction. Then you can find the direction of Net force as described earlier.
Q: When we are dealing with circular motion, we are asked to draw out the different views of the problem diagram. How should we establish which views (end, front, side, top) help better understand the problem? Or how can we ensure they are drawn correctly?
A: For the basics of Three View Diagrams, you can refer to this video clip: https://www.youtube.com/watch?v=xPj2qBLnbi4
I gave a brief review in lecture last week.
As for using the diagrams in Circular Motion problems, most likely we use Top View diagram to visualize the Motion (Velocity in the Tangential direction and Centripetal Acceleration/Force in the Radial direction) and use Front or End view diagram to analyze the forces (Normal, Weight, Friction…). On the Top view diagram, the Vertical direction (z-axis) looks like a Dot. On the Front or End view diagram, the Tangential direction looks like a Dot. If you can visualize the above 2 dots in your mind, your 3-D imagination is solid! Unfortunately, there is no universal easy way to ensure your drawing is correct. You have to use your 3-D imagination to compare Different View diagrams for consistency! It is helpful to do some practice to convert one 3-D diagram to three Different view diagrams and also do the conversion in the opposite way.
