Relationship between Rectilinear and Angular Motion

In summary, the concept being discussed is the use of rectilinear and angular motion in problem solving. The first example involves calculating the time it takes to complete one pass around a pipe of a given diameter, while the second example involves determining the speed of a belt passing over a pulley based on the speed and diameter of the pulley. The equations s=r*angle and v=rw are used in these calculations.
  • #1
smashbrohamme
97
1
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 can't 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 can't 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 I am 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 can't seem to get any of this stuff. I need a breakdown of this please.
 
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  • #2
smashbrohamme said:
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 can't 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 can't 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 I am 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?
 
  • #3
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 don't 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.
 
  • #4
smashbrohamme said:
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 don't 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.
 
  • #5


I can understand your confusion with the relationship between rectilinear and angular motion. Let me break it down for you in simpler terms.

Rectilinear motion refers to the movement of an object in a straight line. This can be measured in terms of distance (such as inches or meters) per unit of time (such as minutes or seconds). In your first example, the automatic pipewelder is moving in a straight line around the pipe at a speed of 40 inches per minute.

On the other hand, angular motion refers to the movement of an object along a circular path. This can be measured in terms of angle (such as degrees or radians) per unit of time (such as minutes or seconds). In your first example, the pipe has a diameter of 4 feet, which means it has a circumference of 48 inches. This is where the angular motion comes into play.

To solve the first problem, you need to use the relationship between linear and angular motion. We know that the speed of the pipewelder is 40 inches per minute and the pipe has a circumference of 48 inches. This means that the pipewelder will complete one full rotation (360 degrees or 2π radians) in 48 inches. Therefore, the angular speed (ω) of the pipewelder can be calculated as:

ω = linear speed / radius
ω = 40 in/min / (48 in / 2π)
ω = 2π/48 rad/min

Now, to find the time it takes for one pass around the pipe, we can use the equation:

time = angle / angular speed
time = 2π / (2π/48) min
time = 48 min

This is the time it takes for the pipewelder to complete one full rotation around the pipe. However, the question asks for the time to complete one pass, which is half a rotation. So the actual time would be 48 min / 2 = 24 min.

For the second problem, we can use a similar approach. The stroboscope measures the speed of the puller (linear speed) at 1600 rpm (revolutions per minute). But we need to find the speed of the belt (linear speed) passing over the pulley. We also know that the pulley has a diameter of 200 mm, which means it has a circumference of 2π * 200 mm = 400π mm.

 

1. What is the relationship between rectilinear and angular motion?

The relationship between rectilinear and angular motion is that they are both types of motion that an object can have. Rectilinear motion refers to the motion of an object in a straight line, while angular motion refers to the motion of an object around a fixed point or axis. These types of motion are related because an object can have both rectilinear and angular motion simultaneously, such as a wheel rolling forward while also rotating on its axis.

2. How are rectilinear and angular motion related to each other?

Rectilinear and angular motion are related to each other because they both involve the displacement and velocity of an object. In rectilinear motion, the displacement and velocity are measured in a straight line, while in angular motion, they are measured around a fixed point or axis. Additionally, both types of motion can be described using the equations of motion and Newton's laws of motion.

3. Can an object have both rectilinear and angular motion at the same time?

Yes, an object can have both rectilinear and angular motion at the same time. This is known as compound motion, where an object's motion can be broken down into both rectilinear and angular components. An example of this is a car driving in a straight line while also turning its wheels to go around a curve.

4. How does the direction of motion differ between rectilinear and angular motion?

The direction of motion in rectilinear and angular motion differs in that in rectilinear motion, the direction is defined by a straight line, while in angular motion, the direction is defined by a circular path around a fixed point or axis. This means that in rectilinear motion, the direction can be forward, backward, left, or right, while in angular motion, the direction can be clockwise or counterclockwise.

5. What are some real-life examples of rectilinear and angular motion?

Some real-life examples of rectilinear motion include a car driving in a straight line, a person walking, or a ball rolling down a hill. Some examples of angular motion include a spinning top, a swinging pendulum, or a Ferris wheel rotating on its axis. Many objects in our daily lives exhibit both rectilinear and angular motion, such as a bicycle rolling forward while also rotating its wheels.

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