Angular speed is the angle turned per unit of time: one revolution is 2π radians. Linear speed is the distance a point travels, v = rω, so a point further from the center moves faster.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
A wheel turns at 8 revolutions per minute. Find its angular speed in radians per second.154π radians per second
A wheel of radius 5 inchesturns at 40 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.400π inches per minute
A point on the rim of a wheel of radius 13 feetmoves at 520π feet per minute. How many revolutions per minute is the wheel making?20 revolutions per minute
A wheel turns at 18 revolutions per minute. Find its angular speed in radians per minute.36π radians per minute
A point on the rim of a wheel of radius 7 feetmoves at 252π feet per minute. How many revolutions per minute is the wheel making?18 revolutions per minute
A wheel of radius 6 inchesturns at 120 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.1440π inches per minute
A point on the rim of a wheel of radius 6 feetmoves at 288π feet per minute. How many revolutions per minute is the wheel making?24 revolutions per minute
A wheel of radius 14 inchesturns at 10 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.280π inches per minute
A point on the rim of a wheel of radius 11 feetmoves at 220π feet per minute. How many revolutions per minute is the wheel making?10 revolutions per minute
A wheel of radius 5 inchesturns at 60 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.600π inches per minute
A point on the rim of a wheel of radius 14 feetmoves at 700π feet per minute. How many revolutions per minute is the wheel making?25 revolutions per minute
A wheel of radius 7 inchesturns at 45 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.630π inches per minute
A wheel turns at 36 revolutions per minute. Find its angular speed in radians per second.56π radians per second
A wheel turns at 25 revolutions per minute. Find its angular speed in radians per minute.50π radians per minute
A wheel of radius 13 inchesturns at 120 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.3120π inches per minute
A point on the rim of a wheel of radius 11 feetmoves at 2640π feet per minute. How many revolutions per minute is the wheel making?120 revolutions per minute
A wheel of radius 9 inchesturns at 50 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.900π inches per minute
A point on the rim of a wheel of radius 5 feetmoves at 900π feet per minute. How many revolutions per minute is the wheel making?90 revolutions per minute
A point on the rim of a wheel of radius 13 feetmoves at 936π feet per minute. How many revolutions per minute is the wheel making?36 revolutions per minute
A wheel of radius 9 inchesturns at 12 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.216π inches per minute
A wheel of radius 3 inches turns at 20 rpm. Linear speed of the rim?
ω = 20 × 2π = 40π radians per minute.
v = 3 × 40π.
The answer is 120π inches per minute.
Where students go wrong
Using revolutions instead of radians in v = rω. The formula only works with the angle in radians.
Also called angular velocity, linear velocity or rpm to radians.
Questions about these worksheets
Yes. Every linear and angular speed sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the linear and angular speed questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Using revolutions instead of radians in v = rω. The formula only works with the angle in radians.