linear velocity hw question

[xdem713o]

My hw question states, "determine the velocity of a truck (in miles per hour) with 40 inch wheels, if the angular velocity of the wheels is 30 rpm(revolutions per minute).

So far, this is what I have. I am using the formula v=rW (the w is supposed to be that weird w that denotes angular velocity)

(40 in.) (30 rpm/min) (2pi/1 rev) (60 min/1 hr) (1 mi/ 63360) I followed an example in my book to a similar problem and it had this set up. I am getting 7.13 mph as my answer. But this is not correct. I understand that why I am multiplying 40 in and 30 rpm but 2 pi, 60 minutes and 1 mi.. in order to convert these to mph. But I'm just not getting the right answer.

 

[Deleted member 4993]

My hw question states, "determine the velocity of a truck (in miles per hour) with 40 inch wheels, if the angular velocity of the wheels is 30 rpm(revolutions per minute).

So far, this is what I have. I am using the formula v=rW (the w is supposed to be that weird w that denotes angular velocity)

(40 in.) (30 rpm/min) (2pi/1 rev) (60 min/1 hr) (1 mi/ 63360) I followed an example in my book to a similar problem and it had this set up. I am getting 7.13 mph as my answer. But this is not correct. I understand that why I am multiplying 40 in and 30 rpm but 2 pi, 60 minutes and 1 mi.. in order to convert these to mph. But I'm just not getting the right answer.

What is the right answer?
What does 40 in wheel mean (radius or diameter)?

 

[xdem713o]

Apparently, the right answer is 3.57. And as for 40 inches, I'm assuming its the diameter.. since it just says 4o inch wheels.

 

[Mrspi]

My hw question states, "determine the velocity of a truck (in miles per hour) with 40 inch wheels, if the angular velocity of the wheels is 30 rpm(revolutions per minute).

So far, this is what I have. I am using the formula v=rW (the w is supposed to be that weird w that denotes angular velocity)

(40 in.) (30 rpm/min) (2pi/1 rev) (60 min/1 hr) (1 mi/ 63360) I followed an example in my book to a similar problem and it had this set up. I am getting 7.13 mph as my answer. But this is not correct. I understand that why I am multiplying 40 in and 30 rpm but 2 pi, 60 minutes and 1 mi.. in order to convert these to mph. But I'm just not getting the right answer.

In ONE revolution, a point on the tire moves through the circumference of the tire. If the diameter of the tire is 40 inches, the circumference is 40*2 pi inches.

In 30 revolutions, the point moves 30 times as far as it does in one revolution, or 30*40*2pi inches.

Ok...now you know that the velocity of a point on the tire is 30*40*2pi inches/minute

Convert that to miles per hour, and you should get the correct answer:

(30*40*2 pi inches)/1 minute * 60 minutes/1 hour * 1 foot/12 inches * 1 mile / 5280 feet

 

[wjm11]

My hw question states, "determine the velocity of a truck (in miles per hour) with 40 inch wheels, if the angular velocity of the wheels is 30 rpm(revolutions per minute).

So far, this is what I have. I am using the formula v=rW (the w is supposed to be that weird w that denotes angular velocity)

(40 in.) (30 rpm/min) (2pi/1 rev) (60 min/1 hr) (1 mi/ 63360) I followed an example in my book to a similar problem and it had this set up. I am getting 7.13 mph as my answer. But this is not correct. I understand that why I am multiplying 40 in and 30 rpm but 2 pi, 60 minutes and 1 mi.. in order to convert these to mph. But I'm just not getting the right answer.

Good job on the set-up and calculation. But…

Apparently, the right answer is 3.57. And as for 40 inches, I'm assuming its the diameter…

Notice that your answer is off by a factor of 2. Does that raise any suspicions? If 40” is the diameter, then the radius is 20”. If you use that in your calculation, instead of 40”, you’ll get the right answer. (The “r” in v=rW means radius.)

Be sure to use the correct roundoff when stating your answers.

Good job though. You just had a small mistake/misinterpretation of the problem.

 

[xdem713o]

Ok, I got 3.56 on my calculator and rounded it up to 3.57. Thanks for help!! I'm really glad I found this website!