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Nutation

You might see a gyroscope “wobble” while precessing. It might look like the precession is unstable and “nods” up and down. Such “nodding” – let’s…

Spinning & precession

Why does a spinning toy top not fall over? How can a plate balance on a stick only when spinning fast? And why doesn’t the…

Newton’s 3rd law vs 2nd law

Newton’s 2nd law told us that unbalanced forces cause acceleration. But Newton’s 3rd law now tells that forces always come in pairs, equal but opposite…

Reaction forces

Take a step. You exert a stepping force on the ground. It is of course at an angle. The horizontal part $F_{\text{step}\parallel}$ pushes along the…

Elastic & inelastic collisions

‘Jumping on a trampoline’ and ‘jumping on asphalt’ are of course two very different feelings. The “impact” with the surface is very different. In one…

Rotational stability & gyroscope

The phenomenon of precession explains why a spinning top keeps spinning, and even why a tilted spinning top keeps that same tilt (while rotating –…

Angular momentum conservation

Just like we have a linear momentum conservation law telling us how the sum of all momentum never changes (the same before and after any…

Angular momentum

We have linear position $\vec s$, velocity $\vec v$ and acceleration $\vec a$ as well as their equivalent angular position $\vec \theta$, angular velocity $\vec…

Momentum conservation

Collisions never hurt just one thing. A crashing car never just damages itself. There is always a second object involved, which is also hurt or…

Newton’s 2nd law with momentum

The carried tomato and the falling tomato both weigh the same. Carrying the tomato means that your hand is doing the tough task of counteracting…

Momentum

Carrying a tomato takes effort due to its weight. Catching a tomato takes more effort due to not only its weight but also the impact…

Centre-of-mass

Throw a frees-bee. It flies at some speed $v$. But exactly what is moving at that speed $v$? It spins while flying, so each “particle”…

Yo-yo

A yo-yo has, as we all know, a centre axle. Pulling the string means pulling a bit away from the centre. That creates a torque,…

Rolling (advanced)

Let go of a wooden block in a smooth bowl. It slides up the other side. Let go of it in a rough bowl, and…

The wheel & rolling

Place a Christmas star on the table. Push it forward. It “rolls” a few “steps”. The spike that touches the table didn’t slide – the…

Newton’s 1st & 2nd law in rotation

‘Forces cause acceleration dampened by inertia (mass)’. That is Newton’s 2nd law: $$\sum \vec F=m\vec a\tag{2nd law}$$ Does ‘angular forces (torques) similarly cause angular acceleration dampened…

Moment-of-inertia

Stuff is “tough” to move around. We called this inertia earlier. “Throwing toughness”, or we could say linear inertia, when throwing a heavy stone or…

Torque

To tighten the bolt, you pull a wrench. Do you pull close or far from the bolt – from the axis-of-rotation? Far, of course. Everyone…

Geometric bonds

Carrying a spinning toy top around the room on a tray doesn’t affect its spinning. The top’s translation and rotation are not connected or coupled.…

Rotation & translation

Stuff can move – like a falling stone – ‘some metres’ and with ‘some metres-per-second’ etc. Stuff can also rotate – like a spinning merry-go-round. But…

Elastic force (Hooke’s law)

You want to bungee jump off a 50-metre bridge. You want to fly downwards, barely scrape the water and then be jolted back up by…

Static friction

We all know the childhood issue of sitting on a slide and not sliding. After a little “kink” with the body, sliding starts. But what…

Kinetic friction models

Friction is not only due to ‘“peaks” sinking into “valleys”’. The two touching surfaces are rough, so their “peaks”, or asperities, are touching. When touching,…

Kinetic friction

Your hand does not slide as easily over a wooden table as over a frozen icy lake. There is more resistance against the sliding. More…

Normal force

We all know that surfaces are able to “hold back” when carrying stuff and when burdened, squeezed or pushed. If they couldn’t, they would break.…

Weight

A most obvious fact is: ‘everything falls if not held up’. We call that tendency to fall gravity.

Fundamental forces

After centuries of research into known forces and search after new ones, people have come to realise that all forces we know of are “versions”…

Known forces

Three main laws of how things move and interact were discovered by Newton. Newton’s laws of motion they are called, but often they are simply…

Reference frames

If a bus brakes, it feels like you are squeezed forward in your seat – that is just a non-existing pseudo-force. You think you are…

Pseudo-forces

When the bus brakes, you feel pushed forward in your seat. When the car turns, you feel squeezed to the opposite side. When a merry-go-around…

Newton’s 1st law (no change)

When there is no acceleration, $\vec a=0$, Newton’s 2nd law of course becomes: $$\sum \vec F=0$$ And this is actually what we would call Newton’s…

Newton’s 2nd law (motion change)

‘A spaceship accelerates off into outer space.’ We can imagine the scenario. The rocket forces cause the spaceship to accelerate and speed up. ‘Suddenly the…

Inertia & mass

Throw around with stuff and you quickly realize that some stuff is “tougher” than other. Not just from being bigger but really from being “tougher”…

Force

Mom throws an orange to the kid. He catches it and puts in the grocery basket dad is carrying. They are affecting the objects; creating,…

Centrifugal effect

A passenger in a car feels “squeezed” to the side when the car turns. And to which side? To the opposite side than the turning;…

Elliptic motion

How can the satellite stay in orbit up there? Why doesn’t it fall?

Circular motion

A satellite in orbit, the child on the merry-go-around, the motorcycle riders on a Wall of Death, a game of tetherball and so on are…

Turning & speeding

While driving, your velocity changes when you speed up (or slow down) and also when you turn.

Throwing & free falling

An orange, shot from an orange cannon, flies in a bow through the air. At any moment it has a position $\vec s=(s_x,s_y)$, a velocity…

Motion equations

You drive with ‘10 metres-per-second’ (start speed, let’s symbolise it $v_0$ since it is the speed after ‘zero seconds‘) and speed up with ‘2 extra…

Gravity

Bring a loaded gun, a tennis ball, a barbell and a bathing ball and throw the tennis ball straight sideways, shoot the bullet straight sideways,…

Changes of changes

Velocity is change in position: $\vec v=\vec s^{\prime}$. Acceleration is change in velocity: $\vec a =\vec s^{\prime \prime}$. Acceleration can of course change as well;…

Acceleration

You are driving a steady $20\,\mathrm{m/s}$ ($72 \,\mathrm{km/hr}$) but a car behind you is rushing. You push the gas pedal and slowly speed up by…

Velocity

Bang! The rudder hits a rock and breaks. You can’t steer your boat! The propeller just moves you north now with $4\,\mathrm{m/s}$. The harbour is…

Fundamental properties

In the Existence discipline we called time $t$, position $\vec s$ and quantity $n$ fundamental properties. ‘Fundamental’, because we can’t explain or describe them from…

Speed

The distance from school to bagel store is 2 kilometres, $\Delta s=s_\text{end}- s_\text{start}=2000\,\mathrm m$. Your coffee break is 500 seconds long (a bit below 10…

Curvature conservation

A pizza slice is initially flat. Its principle curvatures are both zero, so its Gaussian curvature is $G=\underbrace{k_\text{smallest}}_0\cdot \underbrace{k_\text{largest}}_0=0$.

Shape

A new garden sculpture fills a certain amount of cubic metres (volume) but whether it fits in the trunk also depends on the shape. Size…