Linear Speed/Angular Speed

[mathxyz]

What is the difference between linear speed and angular speed?
Does each have a formula?

A car is moving at a rate of 50 miles per hour and the radius of its wheels is 2.5 feet.

A) find the number of revolutions per minute the wheels are rotating.

B) Find the angular speed of the wheels in radians per minute.

 

[Guest]

What is the difference between linear speed and angular speed?

Linear speed is the rate at which something's position changes. Angular speed is the rate at which an angle changes.

A) find the number of revolutions per minute the wheels are rotating.

Every minute, the care moves 50 miles, so every minute, 50 miles of the tire pass over the ground. The circumference of the tire is 5pi, so how many times does the circumference of the tire pass over the ground in a minute?

B) Find the angular speed of the wheels in radians per minute.

Now that you've done A), you know how many revolutions there are in a minute. Each of those is an angle of 2pi, so through what angle does the tire rotate in a minute?

 

[tkhunny]

A car ... and the radius of its wheels is 2.5 feet.

Whoa! Those are serious wheels! What is the outside radius of the tires?

 

[mathxyz]

ok

I will review your notes some more. I will need the formula for linear speed and angular speed.