# Circular motion - finding revolutions?

#### wschmidt22

i've been struggling for hours upon hours attempting to find the answer to simple problems and i'm extremely depressed..

how do i find the amount of revolutions if i'm given the constant angular acceleration (rad/s^2) and the time (seconds)?

#### Doc Al

Mentor
Could you solve the analogous linear problem? If you were given the time and a constant linear acceleration, could you solve for the distance traveled? It's the same problem.

Angular quantities obey kinematic equations analogous to those obeyed by linear quantities. See: http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#rlin"

You also need to be able to convert from radians to revolutions. How are they related?

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#### wschmidt22

i've spent hours crunching numbers into equations.. find total radians then divide by 2*pi? i'm burnt out.. how about you just tell me what i do

#### wschmidt22

or at least put it into english for me, to get the amount of rotations, when you have acceleration and time.. you need to do what?

#### Doc Al

Mentor
How about you post the exact problem you are trying to solve and show what you've done so far.

You didn't answer my question: Do you know how to solve the linear kinematic problem?

[I'll move this to HW: Intro Physics.]

#### wschmidt22

i'm simply asking the proper method for finding revolutions when given accel and time. i've struggled for hours and i'm pretty fed up.. if you wanna do the whole "answer my question with a question" thing, then go for it dude.. i'm just looking for a little help.

and yeah you just plug the values in the equation.. pretty straightforward.

#### Doc Al

Mentor
and yeah you just plug the values in the equation.. pretty straightforward.
What equation are you using?

#### wschmidt22

you're killin me here doc.. i've tried everything.. i know this is easy. tell me this: do i need to find the radius? if so, how do i do that using rad/s? is it vT/(2*pi)? c'mon doc.. work with me here.

#### Doc Al

Mentor
Let me get this straight. You've worked on this for hours, yet you won't take 5 minutes to state the exact problem and show what you've done?

No, you don't need the radius. (At least as far as I can tell, since you still haven't stated the full problem.) So far, it sounds like a kinematics problem. But who knows?

(FYI: The kinematics equations are all contained in that link I gave.)

#### wschmidt22

A wheel starts from rest with a constant angular acceleration of 2.50 rad/s2 and rolls for 7.72 seconds.

How many revolutions does it go through?

answer is 11.86.. how the hell do you get there?

#### Doc Al

Mentor
There are several ways to go:

Look for a kinematic equation that relates distance/displacement (or angle) to acceleration and time. Here's a list: https://www.physicsforums.com/showpost.php?p=905663&postcount=2"

Or you can just figure out the average angular speed and use that to figure out the angle swept out during that time.

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#### wschmidt22

k. just used displacement & time:

x = x_0 + v_0 t + (1/2) a t^2

then divided by 2*pi

now how about when they give the radius and time? which equations do i need there?

ex:

While riding on a Ferris wheel at a constant speed, you measure on your stopwatch that it takes the wheel 41.87 seconds to finish one cycle. The radius of the wheel is 15.20 meters. What is the angular velocity of the wheel's rotation?

#### zgozvrm

Could you solve the analogous linear problem? If you were given the time and a constant linear acceleration, could you solve for the distance traveled? It's the same problem.
Let's say a truck is accelerating at a constant rate of 2 [itex]m/s^2[/tex] and is traveling in a straight line.
How far does the truck travel in 5 seconds?

#### Doc Al

Mentor
k. just used displacement & time:

x = x_0 + v_0 t + (1/2) a t^2

then divided by 2*pi
Good.

now how about when they give the radius and time? which equations do i need there?

ex:

While riding on a Ferris wheel at a constant speed, you measure on your stopwatch that it takes the wheel 41.87 seconds to finish one cycle. The radius of the wheel is 15.20 meters. What is the angular velocity of the wheel's rotation?
Since you're only asked about angular velocity, the radius is irrelevant. And since the velocity is constant, use the rotational analog of distance = velocity*time.

#### Doc Al

Mentor
Let's say a truck is accelerating at a constant rate of 2 [itex]m/s^2[/tex] and is traveling in a straight line.
How far does the truck travel in 5 seconds?
That depends on its initial velocity. But you'd use the same kinematic equation.

#### zgozvrm

That depends on its initial velocity. But you'd use the same kinematic equation.
That's my point ... there is no initial velocity given in the original question! (Just acceleration and time)

#### Doc Al

Mentor
That's my point ... there is no initial velocity given in the original question! (Just acceleration and time)
That's why I kept insisting that the full question be posted. And it was...
A wheel starts from rest...

#### zgozvrm

My bad! I made my post before updating my browser so didn't see that.

I was trying to help the OP see that either the question was incomplete or that the answer was that you couldn't give the displacement based on the data given.

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