Angular velocity

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rachelmaddie

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Hi. I need my work checked please.
8B2A31BE-2064-49C1-BBC5-1CB7C2A78A6B.jpeg

First, find the circumference of the wheel
C = 2πr

We know that the radius is half of the diameter.
r = 30/2 = 15 inches

Substitute this into the equation:
C = 2π(15)
C = 30π inches

Pi (π)= 3.14
C = 30(3.14) = 94.2 inches

Note that the circumference of the wheels represent one revolution.
Convert 59 miles per hour to inches per minute
59 mi/hr = 59*63, 360/60 = 62, 304 in/min

Set up a proportion to find the number of revolutions:
revolution/inches = revolution/inches
We know that 1 mile = 63, 360 inches
1/94.2 = x/62,304
x = 62,304/94.2
x = 661.4 rev
Therefore, 62,304 in/min = 661.4 in/min = 661.4 rpm

Solution: 661.4 revolutions per minute (rpm)
 
rachelmaddie said:
Hi. I need my work checked please.
View attachment 20814

First, find the circumference of the wheel
C = 2πr

We know that the radius is half of the diameter.
r = 30/2 = 15 inches

Substitute this into the equation:
C = 2π(15)
C = 30π inches

Pi (π)= 3.14
C = 30(3.14) = 94.2 inches

Note that the circumference of the wheels represent one revolution.
Convert 59 miles per hour to inches per minute
59 mi/hr = 59*63, 360/60 = 62, 304 in/min

Set up a proportion to find the number of revolutions:
revolution/inches = revolution/inches
We know that 1 mile = 63, 360 inches
1/94.2 = x/62,304
x = 62,304/94.2
x = 661.4 rev
Therefore, 62,304 in/min = 661.4 in/min = 661.4 rpm

Solution: 661.4 revolutions per minute (rpm)
Click to expand...
Have you been taught the following equation:

linear velocity of the center of the wheel = (angular velocity of the wheel) * (radius of the wheel)

Generally, angular speed is expressed as radians/second.
 
rachelmaddie said:
… I need my work checked please.
Click to expand...
Hi Rachel. Your original work looks okay. Your answer is a bit off because of rounding error.

The exercise doesn't specify the number of decimal places to report, in the answer. You chose to round to the nearest tenth of an rpm. That's fine, but it means that you need to keep more digits when using intermediate results.

rachelmaddie said:
30(3.14) = 94.2
Click to expand...
You can either use the calculator's memory or recall feature, to carry forward all of its decimal digits (something like 94.2477796), or you can write down 94.248 (i.e., carry three places, instead of one).

rachelmaddie said:
Set up a proportion to find the number of revolutions:
revolution/inches = revolution/inches
Click to expand...
That's okay. However, we know it's a division problem because we're interested in how many 94.248-inch circumferences it takes to form 62304 inches (the distance moved in one minute).

62304/94.248

?
 
rachelmaddie said:
Hi. I need my work checked please.
View attachment 20814

First, find the circumference of the wheel
C = 2πr

We know that the radius is half of the diameter.
r = 30/2 = 15 inches

Substitute this into the equation:
C = 2π(15)
C = 30π inches

Pi (π)= 3.14
C = 30(3.14) = 94.2 inches

Note that the circumference of the wheels represent one revolution.
Convert 59 miles per hour to inches per minute
59 mi/hr = 59*63, 360/60 = 62, 304 in/min

Set up a proportion to find the number of revolutions:
revolution/inches = revolution/inches
We know that 1 mile = 63, 360 inches
1/94.2 = x/62,304
x = 62,304/94.2
x = 661.4 rev
Therefore, 62,304 in/min = 661.4 in/min = 661.4 rpm

Solution: 661.4 revolutions per minute (rpm)
Click to expand...
Can I keep this?
 
rachelmaddie said:
Hi. I need my work checked please.
View attachment 20814

First, find the circumference of the wheel
C = 2πr

We know that the radius is half of the diameter.
r = 30/2 = 15 inches

Substitute this into the equation:
C = 2π(15)
C = 30π inches

Pi (π)= 3.14
C = 30(3.14) = 94.2 inches

Note that the circumference of the wheels represent one revolution.
Convert 59 miles per hour to inches per minute
59 mi/hr = 59*63, 360/60 = 62, 304 in/min

Set up a proportion to find the number of revolutions:
revolution/inches = revolution/inches
We know that 1 mile = 63, 360 inches
1/94.2 = x/62,304
x = 62,304/94.2
x = 661.4 rev
Therefore, 62,304 in/min = 661.4 in/min = 661.4 rpm

Solution: 661.4 revolutions per minute (rpm)
Click to expand...

I think the assumptions are not properly established, so I am going to first assume two things :
1) The axle-truck system is a rigid body (they all perfectly move together).
2) The wheel pure-rolls on the ground, i.e the velocity of the point of contact of any wheel and the ground is zero (cause the ground is our refrence frame)
Now, from (1) the linear speed of the axle is the same as the given speed of any point on the truck as it purely translates, so let's call it v, and it's angular velocity is w.
Due to pure rolling (2) and from basic vector analysis, The velocity of the point of contact is given by V-rw = 0 where r is the radius of the wheel.
Thus, w = v/r
 
I apologize. I got confused between the different comments. Should I keep my original work or stick with the photo?
 
rachelmaddie said:
I apologize. I got confused between the different comments. Should I keep my original work or stick with the photo?
Click to expand...
Your approach works for constant angular velocities. So follow that, deal with units appropriately. I assumed you asked it as a physics problem.
 
rachelmaddie said:
Hi. I need my work checked please.
View attachment 20814

First, find the circumference of the wheel
C = 2πr

We know that the radius is half of the diameter.
r = 30/2 = 15 inches

Substitute this into the equation:
C = 2π(15)
C = 30π inches

Pi (π)= 3.14
C = 30(3.14) = 94.2 inches

Note that the circumference of the wheels represent one revolution.
Convert 59 miles per hour to inches per minute
59 mi/hr = 59*63, 360/60 = 62, 304 in/min

Set up a proportion to find the number of revolutions:
revolution/inches = revolution/inches
We know that 1 mile = 63, 360 inches
1/94.2 = x/62,304
x = 62,304/94.2
x = 661.4 rev
Therefore, 62,304 in/min = 661.4 in/min = 661.4 rpm

Solution: 661.4 revolutions per minute (rpm)
Click to expand...
Should I keep this?
 
Otis said:
I do not think that you "should" keep the rounding errors.

I think that you "should" fix them.

?
Click to expand...

Is this good?

First, find the circumference of the wheel
C = 2πr

We know that the radius is half of the diameter.
r = 30/2 = 15 inches

Substitute this into the equation:
C = 2π(15)
C = 30π inches

Pi (π)= 3.14
C = 30(3.14) = 94.248 inches

Note that the circumference of the wheels represent one revolution.
Convert 59 miles per hour to inches per minute
59 mi/hr = 59*63, 360/60 = 62, 304 in/min

Set up a proportion to find the number of revolutions:
revolution/inches = revolution/inches
We know that 1 mile = 63, 360 inches
1/94.2 = x/62,304
x = 62304/94.248
x = 661.0 rev
Therefore, 62,304 in/min = 661.0 in/min = 661.0 rpm

Solution: 661.0 revolutions per minute (rpm)
 
rachelmaddie said:
30(3.14) = 94.248
Click to expand...
30(3.14) = 94.2, not 94.248

Write 30π = 94.248, instead.

That shows we've used a scientific calculator to evaluate 30(π) and that we've rounded the calculator's result (something like 94.247780) to three decimal places. (Some people prefer to say "approximately equal to", so you might also see it written as 30π ≈ 94.248)

rachelmaddie said:
… 62304/94.248
… 661.0 rev
Click to expand...
62304/94.248 is good, but 661.0 is not properly rounded.

What calculator are you using? What does the display show, when you divide 62304 by 94.248?

By the way, the correct unit is rpm, not rev.

?
 
Otis said:
30(3.14) = 94.2, not 94.248

Write 30π = 94.248, instead.

That shows we've used a scientific calculator to evaluate 30(π) and that we've rounded the calculator's result (something like 94.247780) to three decimal places. (Some people prefer to say "approximately equal to", so you might also see it written as 30π ≈ 94.248)


62304/94.248 is good, but 661.0 is not properly rounded.

What calculator are you using? What does the display show, when you divide 62304 by 94.248?

By the way, the correct unit is rpm, not rev.

?
Click to expand...
This is the decimal I get when I calculate it,
661.06442577
 
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