Thread: word problem

A truck is moving at a rat of 90 kilometers per hour, and the diameter of its wheels is 1.25 meters. Find the angular speed of the wheels in radians per minute.


Here is what I got so far:

since I need meters I am going to convert kilometers to meters.

so... 90 kilometers * 1000 = 90,000 meters.

Next I need to figure out how many meters is in 60 minutes:

90,000/60 = 1500 meters in 60 minutes

Ok, now I need to find angular speed:

radius = 0.625

I am not sure about this

1500 * 2pi * .625 = 5980.49 radians per minute?

"90,000/60 = 1500 meters in 60 minutes"
You mean, 1500 m/min -----that is the tangential speed at the circumference of the wheel.

You know that
v = w*r
where
v = tangential speed
w = angular speed
r = radius

So,
1500 = w(0.625)
w = 1500 /0.625 = 2400 radians/min ----------answer.

I think should be 1500/(pi*1.25)

Originally Posted by robasc

A truck is moving at a rat of 90 kilometers per hour, and the diameter of its wheels is 1.25 meters. Find the angular speed of the wheels in radians per minute.


Here is what I got so far:

since I need meters I am going to convert kilometers to meters.

so... 90 kilometers * 1000 = 90,000 meters.

Next I need to figure out how many meters is in 60 minutes:

90,000/60 = 1500 meters in 60 minutes

No. 90000 m/h is 90000 meters in 60 minutes because 60 minutes IS an hour. What you have calculated is that the distance moved is 1500 m inone minute. Clearly that was what you meant because that is how you use it below.

Ok, now I need to find angular speed:

radius = 0.625

I am not sure about this

1500 * 2pi * .625 = 5980.49 radians per minute?

In order that the truck move 1500 meters, the circumference of each wheel must have covered 1500 meters. The circumference of a wheel is, of course, 2pi times the radius or 2pi*6.25. If you DIVIDE 1500 by that you determine how many times the wheel turned in a minute. That is, 1500 m/min is 1500/(2pi*6.25) revolutions per minute. Since one turn of a wheel is 2pi radians, to get "radians per minute" multiply by 2pi. That will just cancel the 2p in the first formula (which is why radians are a useful unit!) leaving 1500/6.25 radians per minute.