Video Transcript
What is the symbol of the missing unit U in the formula momentum in units of U equals mass in units of kilograms times speed in units of meters per second?
To answer this question, we recall the important fact that the units on both sides of a formula have to be the same. So U, the units on the left side of our formula, have to be the same as the units of mass measured in kilograms times speed measured in meters per second. To find the units of mass times speed, we recall that the unit of a product of two quantities is the product of the units of the two quantities, where we multiply and divide units as if they were mathematical variables.
So the unit of mass measured in kilograms times speed measured in meters per second would be kilograms times meters per second. We can’t simplify this any further because kilograms, meters, and seconds are all different base units. So the unit of this product is kilogram meters per second. Now kilogram meters per second is the overall unit of the right-hand side of our formula. And since both sides of a formula must have the same units, we must conclude then that U is exactly kilogram meters per second.
