Question

Determine the linear velocity of an object with an angular velocity of 3.7 radians per second at a distance of 10 centimeters from the center.

Answer 1

3.7*.1

Answer 2

So just 37? There's no equation? There's usually the following equation involved -

v = rw

Answer 3

yes

Answer 4

convert cm to m

Answer 5

for m/s

Answer 6

Huh... then why give the equation?

Answer 7

r is 0.1m and w is 3.7rad/s. plug it in the equation

Answer 8

And that's 1.162...

Answer 9

@Astrophysics If you get a sec.

Answer 10

\[v = \omega r \] omega is your angular velocity, v is your linear velocity, and r is your radius

Answer 11

So it's

v = 10(3.7pi)

Answer 12

But that's not one of my available choices.

Answer 13

Because you have to pay attention to the units

Answer 14

So... 10 centimeters?

Answer 15

Do I divide something?

Answer 16

What do you want your answer in

Answer 17

I'm sorry, I've never been good with units.

Answer 18

Centimeters per second?

Answer 19

If I want seconds, do I convert the radians to seconds?

Answer 20

Yes then we just multiply to get the following \[v = 10 cm \times 3.7 \frac{ rad }{ s } = 37 cm/s\]

Answer 21

How would I do that in a calculator though?

Answer 22

?

Answer 23

rad/s = pi/60?

Answer 24

\[1 ~ radian = \frac{ 180 }{ \pi } degrees\] these are separate units we don't have to do anything we just have to multiply the angular speed by the radius

Answer 25

Oh so I have to convert it to degrees?

Answer 26

No, you don't need to convert anything

Answer 27

Then I am absolutely confused.

Answer 28

The radians is an "invisible" unit

Answer 29

So if we have rad/s*m = m/s

Answer 30

So for this one...

Determine the linear velocity of an object with an angular velocity of 5.9 radians per second at a distance of 12 centimeters from the center.


5.9 x 60?

Answer 31

Where did you get 60?

Answer 32

60 seconds?

Answer 33

If I follow the whole

v = rw

I get some insane answer that has nothing to do with my choices.

Answer 34

\[\huge v = \omega r \] your linear velocity here is v, omega (w) is the angular velocity and r is the radius

Answer 35

Why are you using 60 seconds, it's just \[v = (5.9 rad/s) (12 cm)\]

Answer 36

That gives your answer in cm/s

Answer 37

But that's like 222.43

Answer 38

Use your calculator, 5.9*12 = 70.8

Answer 39

Oh.. so I just get rid of the pi

Answer 40

Why are you using pi??

Answer 41

I don't know! I meant the radians symbol thing

Answer 42

all we need is that relationship