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.
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 inches turns at 40 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.400π inches per minute
A wheel of radius 8 inches turns at 30 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.480π inches per minute
A wheel of radius 4 inches turns at 30 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.240π inches per minute
A wheel of radius 6 inches turns at 15 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.180π inches per minute
A point on the rim of a wheel of radius 13 feet moves at 520π feet per minute. How many revolutions per minute is the wheel making?20
A wheel of radius 12 inches turns at 15 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.360π inches 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 feet moves at 252π feet per minute. How many revolutions per minute is the wheel making?18
A point on the rim of a wheel of radius 3 feet moves at 108π feet per minute. How many revolutions per minute is the wheel making?18
A wheel of radius 5 inches turns at 120 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.1200π inches per minute
A point on the rim of a wheel of radius 11 feet moves at 2640π feet per minute. How many revolutions per minute is the wheel making?120
A wheel turns at 90 revolutions per minute. Find its angular speed in radians per minute.180π radians per minute
A wheel turns at 75 revolutions per minute. Find its angular speed in radians per second.25π radians per second
A wheel turns at 45 revolutions per minute. Find its angular speed in radians per minute.90π radians per minute
A wheel of radius 4 inches turns at 24 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.192π inches per minute
A wheel turns at 30 revolutions per minute. Find its angular speed in radians per minute.60π radians per minute
A wheel of radius 13 inches turns at 18 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.468π inches per minute
A point on the rim of a wheel of radius 6 feet moves at 144π feet per minute. How many revolutions per minute is the wheel making?12
A wheel of radius 3 inches turns at 12 revolutions per minute. Find the linear speed of a point on its rim in inches per minute.72π 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.