Over the past 5 years of teaching Physics in Qatar to students from very diverse backgrounds, I have observed a common set of mistakes that almost everyone makes. I incorporate these observations into my sessions to help students avoid them.
I have recorded these mistakes here for the benefit of all students taking Physics I. Each mistake is explained in detail along with strategies on avoiding them wherever applicable.
CHAPTER 2-3: MOTION
1) Sign errors
One of the most common errors in motion problems is using the wrong signs. To avoid this, use a simple rule:
All vectors pointing right/up: (+)
All vectors pointing left/down: (-)
"(-)لو السهم مع الأكسيس, يكون(+). لو عكسه، يكون"
2) Taking velocity = zero when object hits the ground
An object doesn't stop the moment it touches the ground.
It stops about 0.001 seconds after hitting the ground
The human eye can't see this, so objects seem to stop as soon as they hit. Let's fix that with a slow motion video:
Notice the tennis ball continue to move even after touching the ground.
So to avoid this mistake, remember this image.
"Hitting the ground doesn't mean v=0"
3) Equating velocities when two objects "meet" or "hit"
When two objects meet, they have to be at the same place (position). They don't have to be moving with the same velocity.
And when objects have the same velocity, they don't have to be at the same place.
Taking an extreme example: A car is going 80 kph Northwards in Doha and another car is going 80 kph Northwards in London. They have the same velocity. Does that mean they will hit each other? I don't think so!
"When two objects meet or hit, v1 =\= v2, but x1=x2 and y1=y2"
4) Forgetting that constant velocity means acceleration is 0
In a lot of questions, they don't tell you the acceleration directly. They say that the velocity is constant (or provide a constant velocity value)
Which means velocity is not changing
which means the rate of change of velocity is 0 What is rate of change of velocity called? acceleration!
So acceleration is 0.
"Constant velocity means acceleration is 0"
5) Using constant acceleration equations when acceleration is not constant
If acceleration is something like 3 (or 5, or a) it's constant, and you can use equations like v=v0+at.
If it is 3t+4, it is not constant, so you have to use integration to find velocity.
CHAPTER 4-5: FORCES
1) Drawing Normal upwards in all situations
This is an error of habit. When an object is on a flat surface, N is upwards. But the general rule is that Normal is perpendicular to the surface and pushing away.
Normal force doesn't mean "عادي force" or "not so special force". Normal means perpendicular. It has to be perpendicular to the surface.
"Normal is perpendicular to the surface, not up"
2) Being careless with x and y-components of acceleration
Acceleration is a vector, just like the forces that cause it. So if it goes left or down, the x and y components should be negative* To avoid this mistake, always draw your acceleration in your free body diagram and take components for it just like you do for any force.
"Free body diagram isn't complete without acceleration"
3) Reusing solutions for N, T, and fs from a previous situation
Normal, Tension, and static friction are "intelligent" forces. They don't have constant magnitudes. That's why, when you find a magnitude for N or T or fs from part (a), don't use the same value in part (b) because the situation is probably different.
"Don't use Normal/Tension/Stat friction magnitude from part (a) in part (b)"
CHAPTER 6: WORK
Mistakes start getting less frequent from this chapter onward, but there are still some very common ones.
1) Sign errors
When finding total work (by finding work done by each force and then adding), sign errors are very common, so it is a good idea to do a common sense check on your answers.
This image of a man trying to move his car and his two sons "working" alongside might be helpful:
"If the force helps the motion: Work is positive; if it hurts motion: Work is negative. If it doesn't Help: Work is zero"
2) Writing N=mg
When an object is on a flat surface and no vertical forces are acting on it except gravity, then N=mg. In any other situation, N is not mg.
The first situation (N=mg) was very common in Chapters 4 and 5, so when using Normal in chapter 6, 99% of students (including me when I was one) make the mistake of using N=mg directly.
Normal is an "intelligent" force. It's magnitude depends on other forces. So you should always finds it's value from the force equations before using it.
"Never replace 'N' with 'mg' unless you get N-mg=0 from Newton's law"
CHAPTER 7: CONSERVATION OF ENERGY
1) Sign errors with potential energy
When it comes to spring potential energy, a common error is taking it as negative when the spring is compressed. Just..don't do that. It can't possibly be negative because k (spring constant) is always positive and x (compressing/stretching distance) is squared.
For gravitational potential energy (mgh), the main mistake is forgetting to take it as negative when object is below the ground. To avoid this, always mark the ground level in your figure (it doesn't have to be the actual ground).
"Spring potential energy is always positive.
"Always mark ground level in figure. mgh is (-) when your'e below ground level"
2) Writing N=mg when finding Work done by friction
Refer to the same mistake's explanation in Chapter 6 above
CHAPTER 8: CONSERVATION OF MOMENTUM
1) Not taking velocity negative for an object going left or downwards
In my session for this chapter, the third question involves a negative velocity, and 90% of students mess it up (by forgetting to take it as negative). The sign is forgotten as we focus on where to put which velocity in the equation (there can be up to 8 velocity terms involved).
"Remember to check signs of velocities after setting up momentum conservation equation"
2) Messing up the algebra
The most challenging thing in this chapter is solving the equations you set up. You may reach a dead-end from which trying to solve makes equations more complicated. If you avoid the doing the two things shown below, you will avoid all the dead-ends.
a) Avoid square roots
b) Avoid complicated 2ab term (i.e. both a and b are unknown)
REST OF THE CHAPTERS INVOLVING ROTATION
Since the rest of the course after chapter 8 is basically the same concepts repeated for rotational motion, the errors are the same as well. However, if you have practiced the previous chapters well, there are no new errors introduced in the later chapters.