Question

Trig: Angular & Linear Velocity

Determine the number of rpm of a wheel turning 52.8 rad/s

Answer 1

@ranga can you help me? I have no clue what I am doing when it comes to this stuff.

Answer 2

I got the answer of 8.40 but I saw the answer key and it says the answer is: 504.2

Answer 3

52.8 radians = 52.8 / (2pi) revolutions
that is in 1 second.
In i minute, multiply by 60.
52.8 / (2pi) * 60 revolution per minute or rpm.

Answer 4

Well radians is an angular unit which compares arc length to radius. 1 radian is the angle it takes to create an arc length equal to the radius.

That being said, there are 2pi radians for 1 revolution (360 degrees)
So if we have 1 radian/s and we what revolutions/min, we need to do some conversions. Dimensional analysis will be of help here:

\[ \ 52.8 \frac{rad}{s}*\frac{60 \text{seconds}}{1 \text{min}}*\frac{1 \text{ revolution}}{52.8 \text{ radians}}\]

Notice the seconds and radians will cancel out, and we will be left with the unit of rev/min

Answer 5

There are (2pi) radians in 1 revolution. Therefore, 1 radian = 1/(2pi) revolutions
There are 60 seconds in 1 minute. Therefore, 1 second = 1/60 minutes

52.8 radians / second = 52.8 * (1/2pi) revolutions / 1/60 minutes
= 52.8 / (2pi) * 60 revolutions / minute.

Answer 6

= 504.2 rpm

Answer 7

you'll notice my error clearly, sorry about that.

\[ 52.8 \frac{radians}{second}*\frac{60 \text seconds}{1 \text{ minute}}*\frac{1 \text{ revolution}}{2 \pi \text{ radians}} \]

Answer 8

What numbers are you multiplying because I am not getting 504.2...

Answer 9

numerator: 52.8 * 60
denominator: 2(pi)

Answer 10

2pi = 360
or
2pi = 6.28

Answer 11

2pi = 6.28.

Answer 12

2pi = 6.28

Answer 13

In science and engineering you will come across unit conversions a lot. So it will be good to become familiar with how to do these types of problems.

Here we essentially need to convert the units: 52.8 radians / sec = x revolutions / minute
what is x?

2pi radians = 1 revolution.
so 1 radian = 1/(2pi) revolutions.

60 seconds = 1 minute
1 second = 1/60 minutes.

52.8 radians / sec = 52.8 * 1 radian / 1 second = 52.8 * 1/(2pi) revolutions / 1/60 minutes = (52.8 * 60) / (2pi) revolutions / minute or rpm.

Answer 14

So we will always have to ... go from Radians to Revolutions to Minutes

Answer 15

4. What is the angular velocity in radians per minute of a notch on a wheel that makes 24 rotations per second about its axis?

Answer 16

Is this the same?

Answer 17

I have to switch it to revolutions?

Answer 18

pretty much the same procedure as before.

24 rotations / second = x radians / minute. What is x?
so we have to replace rotations by radians
we have to replace seconds by minutes

1 rotation = 2pi radians

60 seconds = 1 minute
1 second = 1/60 minutes.

24 rotations / second = 24 * (1 rotation / 1 second) = 24 * (2pi radians) / (1/60) minutes
= 24 * 2pi * 60 radians / minute

Answer 19

\[\frac{ 24~rotaions }{ second } = 24 *\frac{ 1~rotation }{ 1~second } = 24 * \frac{ 2\pi ~ radians }{ \frac{ 1 }{ 60 }~minute } = 24*2\pi*60~\frac{ radians }{ minute }\]

Answer 20

= 9047.79 radians / minute.

Answer 21

Is 1 rotation = 1 revolution?

Answer 22

They use the words interchangeably in these problems.

But strictly speaking we say: the earth ROTATES on its own axis once a day and it REVOLVES around the sun once a year.

Answer 23

But in these problems 1 rotation = 1 revolution (the words are synonymous)

Answer 24

ok

Answer 25

similar problem you may comes across is to convert miles per hour to feet / second.
What is 60 mph in feet/sec?

Same procedure. 60 miles / hour = 60 * (1 mile / 1 hour)
We need to convert miles to feet in the numerator
We need to convert hour to second in the denominator.

Look up the units and you can do the conversion the same way.

Answer 26

60 * (1 mile / 1 hour) = x feet / second. What is x?

1 mile = 5280 feet
1 hour = 3600 seconds

60 * (1 mile / 1 hour) = 60 * (5280 feet) / (3600 seconds) = 88 feet / second

Answer 27

Is there like websites that practice this stuff?

Answer 28

let me check.

Answer 29

This has some unit conversion examples and exercises: http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienceIntegation-620.htm

Answer 30

Thank You

Answer 31

Here is another: http://www.purplemath.com/modules/units.htm

You are welcome.