Visual Guide — Diagrams, Tables & Concept Maps — Summary

Work Sign Convention at a Glance

θ Range	cos θ	Work Sign	Example
0°	+1	Maximum positive	Free fall (gravity + displacement both down)
0° < θ < 90°	Positive	Positive	Applied force at angle aiding motion
90°	0	Zero	Normal force, centripetal force
90° < θ < 180°	Negative	Negative	Friction opposing sliding
180°	−1	Maximum negative	Braking force exactly opposing motion

Vertical Circular Motion — Force Diagram

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Collision Type Comparison

Property	Elastic	Partly Inelastic	Perfectly Inelastic
Momentum	Conserved	Conserved	Conserved
KE	Conserved	Partially lost	Maximum loss
e	1	0 < e < 1	0
Post-collision	Separate	Separate	Stick together

Energy Conservation Concept Map

Initial KE + Initial PE
        |
        |--- [Conservative forces only] --→ Final KE + Final PE  (= constant)
        |
        |--- [Friction present] --→ Final KE + Final PE + Heat  (= constant)
                                              ↑
                               Mechanical Energy decreases

Useful Number Reference

Quantity	Value
1 horsepower	746 W
1 kWh	$3.6 \times 10^{6}$ J
g (NEET standard)	10 m/ $s^{2}$
Spring PE at x = 0.1 m, k = 200 N/m	1.0 J