Category: 01 Units and Measurement

# 1.8.1 Vector Diagram

# Propagation of Error/Uncertainty

This video provides an overview of the propagation rules:

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Watch this video for a worked example for the product rule.

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Watch this video if you want to see the “proof” of the product rule.

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# 1.2 Prefixes

From the tiniest to the most humongous, this classic powers-of-ten video shows us the mind blowing scale of the natural world. It now has an updated version in the form of an 🍏APPLET which allows you to navigate through the powers-of-ten. Enjoy.

# 105 Resolving Vectors

# 104 Vector Summation/Subtraction

# 103 Propagation of Errors/Uncertainties

# 102 Powers of Ten

From the tiniest to the most humongous, this classic powers-of-ten video shows us the mind blowing scale of the natural world. It now has an updated version in the form of an

🍏APPLET which allows you to navigate through the powers-of-ten. Enjoy.

# 101 Revamped SI Base Units

“On November 16, 2018, in Versailles, France, a group of 60 countries made history. With a unanimous vote, they dramatically transformed the international system that underpins global science and trade. This single action finally realized scientists’ 150-year dream of a measurement system based entirely on unchanging fundamental properties of nature.”

To find out what the fuss is all about, read here.

So how are the SI units defined now? Read here.

# xmPuzzle 003 Six Ants

Question:

Six small ants are each at the vertex of regular hexagon of side 60 cm. The 1st sets out towards the 2nd , the 2nd towards the 3rd … and the 6th towards the 1st, with uniform speed of 5 cm s^{-1}. During their motion each of them always heads towards its respective target ant. How much time has elapsed and what distance do the ants cover before they meet?

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Answer:

24 s, 120 cm.

The motion of the ants will be such that they always form a regular hexagon, which rotates and shrinks over time until it vanishes at the centre. While every ant will be moving in a complicated curved path, we can simplify matter by focusing on just the motion directed towards the centre of the hexagon.

At the start, each ant is 60 cm away from the centre of the hexagon. And their component of velocity in the direction towards the centre is 5 cos 60° = =2.5 cm s^{-1}. So it will take them 60 cm ÷ 2.5 cm s^{-1} = 24 s before they meet.

Since they move at a constant speed of 5 cm s^{-1}, each ant would have moved a total distance of 5 cm s-1 × 24 s = 120 cm.