# Relationship between Rectilinear and Angular Motion

I am having a hard time understanding this concept...

I understand Rectilinear motion consists of a line and Angular Motion is of a Angle.

But I cant seem to understand how to use this for problem solving. I have two examples here that I will give and I have the answers but I cant seem to figure out how to solve them.

1. An automatic pipewelder can weld 40in/min. How long does it take to complete one pass around a pipe 4ft in diameter. *ok first thing i do is convert the 4ft into 48 inches to make it all one unit. Then I simply divide 48inches into 40in/min and its simply 1.2min, The book has 3.77min as the answer so I am assuming I have to use the angular of the pipe but man im stuck on that.

2. By means of a stroboscope, the speed of a puller 200mm in diameter is found to be 1600 rpm. Determine the speed of the belt passing over this pulley.. Ok the answer is 16.7m/s.
I have no idea how to seriously solve this....not even a start really.

I am assuming the equations
s=r*angle

v=rw
alpha=rbeta

are the questions I need, but man I cant seem to get any of this stuff. I need a breakdown of this please.

gneill
Mentor
I am having a hard time understanding this concept...

I understand Rectilinear motion consists of a line and Angular Motion is of a Angle.

Not quite. Angular motion is motion about a center of rotation.

But I cant seem to understand how to use this for problem solving. I have two examples here that I will give and I have the answers but I cant seem to figure out how to solve them.

1. An automatic pipewelder can weld 40in/min. How long does it take to complete one pass around a pipe 4ft in diameter. *ok first thing i do is convert the 4ft into 48 inches to make it all one unit. Then I simply divide 48inches into 40in/min and its simply 1.2min, The book has 3.77min as the answer so I am assuming I have to use the angular of the pipe but man im stuck on that.

The welder is welding along the circumference of the pipe. How long is the circumference of a circle of diameter 48 inches?

2. By means of a stroboscope, the speed of a puller 200mm in diameter is found to be 1600 rpm. Determine the speed of the belt passing over this pulley.. Ok the answer is 16.7m/s.
I have no idea how to seriously solve this....not even a start really.

How fast is the circumference of the puller passing a fixed point immediately above it? In other words, what's the tangential speed of the circumference of the puller? If the belt is in contact with the puller, it must be moving at that same speed, no?

If you know the length of the circumference, and you know that it revolves 1600 times in one minute, how many mm of circumference go by per minute?

ok I now understand the fact that we are talking circular distance now instand of linear...so 48inch diameter is really 150.79inch...and the machine can only do 40inch/min so its 150.79inch/40inchpermin and it will take the machine 3.77mins...simple enough.

Now for part two...I understand the belt is going to have the same speed as the pulley...the pulley is 200dia and going 1600rpm...I still dont really get how to solve this..

200dia equates to 628.3mm so if the pulley is revolving 1600 times per minute you are solving by 1600x628.3mm to equal 1005280?

I am just having a hard time visualizing this..and what equation should I be using for this problem.

gneill
Mentor
Now for part two...I understand the belt is going to have the same speed as the pulley...the pulley is 200dia and going 1600rpm...I still dont really get how to solve this..

200dia equates to 628.3mm so if the pulley is revolving 1600 times per minute you are solving by 1600x628.3mm to equal 1005280?

I am just having a hard time visualizing this..and what equation should I be using for this problem.

You need to keep track of the units involved. 1600 circumferences per minute is the value you have calculated as 1005280. So that's 1005280 mm/min. Convert that to meters per second.