Unit 1: Measurement, Units, and Vectors
The toolkit before the physics starts: how precise a measurement really is, and how a quantity with direction gets added, split, and converted.
7 topics · 24 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Precision and Accuracy in Measurement
- How it worksHow do repeated trials cluster tightly around a value that misses the true answer?
- Common mistakeWhy isn't a measurement with more decimal places automatically the more accurate one?
- Going furtherWhat happens to a set of measurements when you fix a miscalibrated instrument halfway through an experiment?
Your turn1 of 2
A poorly calibrated scale gives the same reading, 152.3 grams, every single time you weigh an object that actually has a true mass of 140 grams, with every trial clustering tightly around that same wrong number. Why can a measurement be precise and still be completely wrong?Scalars and Vectors
- How it worksHow does adding a direction to a speed turn it into a velocity vector?
- Common mistakeWhy isn't distance the same thing as displacement once a path bends?
- Going furtherWhat happens to a runner's displacement after one full lap around a track?
Your turn1 of 2
Knowing a plane flies at 500 miles per hour tells you how fast it's covering ground, but it tells you nothing about whether that plane is headed toward its destination or flying in a completely different direction. Why does saying a plane flies at 500 miles per hour tell you less than you think?Adding Vectors Graphically
- How it worksHow does placing vectors tip to tail give you their sum without any algebra?
- Worked exampleFind the resultant of a 3 m displacement east and a 4 m displacement north using the tip-to-tail method.
- Common mistakeWhy isn't the sum of two vectors just the sum of their lengths?
- Going furtherWhat happens to the resultant vector when the two vectors point in exactly opposite directions?
Your turn1 of 2
Find the magnitude of the resultant of a 21 m displacement east and a 20 m displacement north, added tip to tail.Breaking a Vector into Components
- How it worksHow does a vector split into a horizontal piece and a vertical piece using sine and cosine?
- Worked exampleFind the horizontal and vertical components of a 20 N force applied at 30 degrees above the ground.
- Common mistakeWhy isn't the horizontal component of a vector just the vector's length times its angle?
- Ties togetherHow do vector components reappear the moment you start splitting projectile motion into two axes?
Your turn1 of 2
Find the horizontal component of a 350 N force applied at 57 degrees above the ground.Unit Conversion and Dimensional Analysis
- How it worksHow does multiplying by a chain of conversion factors let units cancel down to the one you want?
- Worked exampleFind how many meters per second 100 kilometers per hour is.
- Common mistakeWhy doesn't a formula's answer mean anything if its units don't cancel down to what you're solving for?
- Going furtherWhat happens to an equation's predicted units when two quantities are accidentally divided instead of multiplied?
Your turn1 of 2
Find how many meters per second 210 kilometers per hour is.Relative Velocity
- How it worksHow does adding a boat's own velocity to the river current's velocity give its actual velocity over the ground?
- Worked exampleFind the resultant velocity of a boat moving at 4 m/s across a river with a current of 3 m/s.
- Common mistakeWhy isn't a boat aimed straight across a river guaranteed to land directly opposite where it started?
Your turn1 of 2
Find the magnitude of the resultant velocity of a boat moving at 10.6 m/s straight across a river that has a current of 9.91 m/s.Significant Figures and Scientific Notation
- How it worksHow do significant figures track how confidently you actually know a measured number?
- Worked exampleFind the correctly rounded answer for 4.52 m multiplied by 2.1 m, respecting significant figures.
- Common mistakeWhy doesn't a calculator's ten-digit display mean your answer is actually that precise?
Your turn1 of 2
Find the correctly rounded answer for 14 m multiplied by 13 m, respecting significant figures.