PHYSICS NOTE — FILLED EXAMPLE AND REUSABLE TEMPLATE
ThetaWave editorial example | September 19, 2026
https://thetawave.ai/blog/how-to-take-physics-notes
Original teaching example, not a student result or AI product output.
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FILLED NOTE
Problem: A 2.0 kg block slides down a fixed, straight, frictionless slope
30 degrees above horizontal. It stays in contact. Ignore air resistance;
use g = 9.8 m/s^2. Treat it as a particle with no other applied forces.
Find downhill acceleration and normal force.

1. PRINCIPLE / SYSTEM
System: block. Newton's second law connects NET force to acceleration.

2. REPRESENTATION
Choose +s downhill and +n perpendicular away from the slope.
Two forces: weight mg vertically down; N perpendicular away from slope.
Weight components: mg sin(theta) downhill; mg cos(theta) into slope.
These components replace mg in the equations; do not add all three.

3. EQUATION / REASONS
Along slope: sum F_s = m a_s (Newton's second law).
mg sin(theta) = m a_s (only the downhill component contributes).
Divide by m: a_s = g sin(theta).
a_s = 9.8 sin(30 degrees) = 4.9 m/s^2 downhill.
Perpendicular: a_n = 0 (contact with fixed, straight slope).
N - mg cos(theta) = 0, so N = mg cos(theta).
N = 2.0 * 9.8 * cos(30 degrees) = 16.97... N, rounded to 17 N.

4. ASSUMPTIONS / LIMITS
Frictionless; constant mass and g; no air resistance; fixed straight
slope; continued contact; angle measured from horizontal.
Redraw forces if rough or externally pulled. If contact is lost,
the zero perpendicular acceleration condition no longer applies.

5. ANSWER / CHECKS
a = +4.9 m/s^2; N = 17 N. Acceleration unit is m/s^2.
Positive means downhill. N < mg = 19.6 N.
As theta tends to 0: a tends to 0 and N tends to mg.
Units alone cannot distinguish sine from cosine.

6. RETRIEVAL CUE
Why is N not equal to mg here? Why only mg sin(theta) along the slope?
Close this note, draw the two forces, state axes, reconstruct equations.

FOUR QUESTIONS — RESET TO ORIGINAL CONDITIONS FOR EACH
1. Only mass changes to 4.0 kg. Find a and N.
2. Add a constant 3.0 N rope pull uphill, parallel to the slope,
   to the original 2.0 kg frictionless case. Find a and N.
3. Choose uphill as positive in the original case. Find signed a.
4. Instead start at rest on a rough slope. Is a = 4.9 m/s^2 justified?

YOUR ANSWERS (fill before reading the key)
1:
2:
3:
4:

REUSABLE NOTE — FILL FOR ONE COURSE PROBLEM
Topic:
Source / chapter / timestamp:
Givens and question:
Principle and system:
Representation / force directions / positive axes:
Equations and reason for each important step:
Assumptions and limits:
Worked answer:
Units / sign / physical-limit checks:
Closed-note retrieval cue:
Changed-condition question:
Checked answer and explanation:

ERROR LOG
Attempt:
Diagnosis:
Smallest repair:
Retest question and outcome:
Next review date:

COMPLETED FICTIONAL ERROR LOG
Attempt: a = g cos(30 degrees) = 8.5 m/s^2 downhill.
Diagnosis: perpendicular component used along slope; units still passed.
Repair: label theta from horizontal and resolve weight on chosen axes.
Retest: flat-slope limit. g sin(0) = 0; g cos(0) incorrectly gives g.
Next task: solve question 2 without opening its answer.

ANSWER KEY — CHECK AFTER YOUR ATTEMPT
1. a = 4.9 m/s^2 downhill; N = 4.0 * 9.8 * cos(30) = 33.95... N,
   rounded to 34 N. Mass cancels in acceleration but not normal force.
2. Downhill net force = 2.0 * 9.8 * sin(30) - 3.0 = 6.8 N.
   a = 6.8 / 2.0 = 3.4 m/s^2 downhill. N stays 17 N because the
   rope force has no perpendicular component. This is not friction.
3. a = -4.9 m/s^2. Negative now means downhill; motion is unchanged.
4. No. To stay at rest, static friction must supply 9.8 N uphill.
   N is about 17 N. Required mu_s >= tan(30 degrees) = 0.577...
   Missing static-friction information prevents deciding if it slides.
   If sliding, a kinetic-friction model is needed for acceleration.

FACT-CHECK SOURCES (original wording and diagram, not reproduced pages)
OpenStax College Physics 2e, sections 4.5 and 4.6:
https://openstax.org/books/college-physics-2e/pages/4-5-normal-tension-and-other-examples-of-forces
https://openstax.org/books/college-physics-2e/pages/4-6-problem-solving-strategies