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Inertio

Newton’s Second Law Physics

\[\vec F_{\text{net}} = m\,\vec a\]
$21.99 USD
$21.99 USD
Obral Habis
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Why is a full shopping cart harder to start than an empty one? Inertio stands firm. Newton’s second law, F = ma, says the net force on a body equals its mass times its acceleration. Double the mass and you need double the force for the same change in motion. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Net force equals mass times acceleration, or more generally the rate of change of momentum. The bigger the mass, the more force you need to change its motion.

Inertio does not move unless you make him, and he makes you work for it.

Newton's second law, the first line, says the net force on a body equals its mass times its acceleration. Net matters: it is the sum of every push and pull. A cart rolling at steady speed on a level floor can have zero net force on it and keep rolling.

Mass is what resists the change. Fill a shopping cart and it takes twice the push to start it as quickly as when it held half as much. That resistance is inertia, and m measures it.

The second line is Newton's own way of putting it: force is the rate of change of momentum. For a body of fixed mass the two forms are the same. The law holds in non-accelerating frames, for speeds far below light and for objects much larger than atoms; beyond that, relativity and quantum mechanics take over.

PUSH ME. I DARE YOU. Inertio will move. Exactly as much as the net force says, and not a bit more.

Equations

\[\vec F_{\text{net}} = m\,\vec a\]
\[\vec F_{\text{net}} = \frac{d\vec p}{dt},\qquad \vec p = m\vec v\]
SymbolMeaningUnit
\(\vec F_{\text{net}}\) net (total) external force on the body \(\mathrm{N}\)
\(m\) mass \(\mathrm{kg}\)
\(\vec a\) acceleration \(\mathrm{m/s²}\)
\(\vec p\) momentum \(\mathrm{kg·m/s}\)
\(\vec v\) velocity \(\mathrm{m/s}\)
\(t\) time \(\mathrm{s}\)

Sources

  1. HyperPhysics — Newton's Laws
  2. Feynman Lectures on Physics Vol. I Ch. 9: Newton’s Laws of Dynamics
  3. Encyclopaedia Britannica — Newton’s laws of motion

Source Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica, Axioms or Laws of Motion, Law II. London: Royal Society (J. Streater).

Field notes

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