See mechanics.
Don't just memorize it.
Every core idea of classical mechanics — motion, force, energy, and waves — lives here as a simulation you can grab, drag, and replay. The equations aren't the physics; they're the caption. The picture is the physics.
Projectile motion is two problems in one
Gravity only pulls down — so the horizontal motion never feels it. Split the launch velocity into components and each axis becomes a problem you already know how to solve: constant velocity across, constant acceleration up-and-down.
Watch the green arrow as it flies: it never changes. Only the red vertical component grows and shrinks. Try θ = 30° and θ = 60° — same range. Complementary angles always land in the same spot.
A force diagram is an argument
Will the block slide? Don't guess — decompose. Tilt gravity's pull into a piece along the ramp and a piece into it. Friction can only fight back up to its limit μN. The moment the along-ramp pull wins, the block moves.
Notice mass never decides the verdict — it cancels from both sides. The tipping point is pure geometry: the block slips exactly when tan θ = μ. Slide θ up slowly and watch the friction arrow max out, then lose.
Energy doesn't vanish — it changes costume
Lift a pendulum and you've stored energy as height. Release it and that energy trades into speed, then back, forever (minus a little tax to air drag). The two bars below always sum to the same total — that's the whole law.
With drag off, the total bar is frozen — the definition of conservation. Turn drag on and watch the total bleed away while the swing shrinks to match. Energy accounting never lies.
Waves don't collide — they add
Two waves passing through each other simply sum, point by point, instant by instant. In phase they reinforce; half a cycle apart they can erase each other completely. That single fact powers noise-cancelling headphones, interference fringes, and beats.
Hit Destructive: identical waves, φ = 180°, and the black sum flatlines — two waves making silence. Then try Beats: nearly-equal frequencies drift in and out of phase, so the sum throbs. That throb is what you hear tuning a guitar.
Now you do the physics
Each problem is solvable with one idea from above. Hints reveal one step at a time — try before you peek, and use the simulators to check your answer.
1 · The cliff throw
A ball is thrown horizontally at 15 m/s from a 20 m cliff. How far from the base does it land? (g = 9.8 m/s²)
20 = ½ · 9.8 · t².t = √(2·20/9.8) ≈ 2.02 s. The horizontal axis just coasts for that long.x = 15 × 2.02 ≈ 30.3 m. Notice the throw speed never entered the falling time.2 · The stubborn crate
A crate sits on a ramp with μ = 0.4. At what angle does it start to slide?
mg sin θ = μ · mg cos θ.mg cos θ and you're left with tan θ = μ.θ = arctan(0.4) ≈ 21.8°. Verify it on the § 02 simulator: set μ = 0.40 and creep the angle past 21°.3 · The swing speed
A pendulum bob is released from a height 0.8 m above its lowest point. How fast is it moving at the bottom?
mgh = ½mv².v = √(2gh).v = √(2 · 9.8 · 0.8) ≈ 3.96 m/s. Drag the § 03 bob up and compare with the “speed at bottom” readout.