# Calculate the angular acceleration and angular velocity

## Homework Statement

Calculate the angular acceleration and angular velocity of a 2kg object rotating in a
circle of 1.5m radius in a time of 3s.

w=v/r
2*pie*r

## The Attempt at a Solution

Now i dont know how to fully work this out, not sure how to apply the forumla.

3 seconds for one complete roatation

360 / 3 = 120 degrees

120 degrees per second

2*pie*r=

9.42m

9.42 / 3 = 3.14ms-1

I know this completes 120 degrees going a distance of 3.14m in a second.

The question is how do i go about completing this question?

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wukunlin
Gold Member
do you mean angular acceleration or centripedal accleration?

what you are using assumes constant angular velocity and angular acceleration is just zero,

but if you want to find centripedal acceleration then after you have found the linear speed, then centripedal acceleration is:

$$a = \frac{v^2}{r}$$

Thanks for your reply, the question is word for word, if im heading in the wrong direction could you point me in the right one please

I need to calculate both angular velocity and angular acceleration

wukunlin
Gold Member
from what I'm seeing you are on the right track, it just feels like the questions has some irrelevant data and vague information

Thanks, i really dont know where to go from there, what is the actual formula or precedure for working this out

just looked in another book and it gives:

w=2*pie*n

that would mean

2*pie*0.3 reccuring(revolutions in one second)

does this sound right?

I dont have a clue what im doing to be honest

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I just understood what you meant by centrepetal acceleration, its the same as angular acceleration(dunno why they called it that and confused things)

my book has:

w2r for angular accel but gives the same answer as your formula.

2.094squared * 1.5= 6.58 rad/s (2dp)

My book says your formula gives it in m/s and w2r should give it in rad/s.

Don't know how that works considering i get the same answer for both, any ideas?

Thanks for all your help so far

tiny-tim
Homework Helper
Hi Joe!

(have a pi: π and an omega: ω )
Calculate the angular acceleration and angular velocity of a 2kg object rotating in a circle of 1.5m radius in a time of 3s.
do you mean angular acceleration or centripedal accleration?

what you are using assumes constant angular velocity and angular acceleration is just zero …
I just understood what you meant by centrepetal acceleration, its the same as angular acceleration(dunno why they called it that and confused things)
no wukunlin is right, and centripetal acceleration and angular acceleration are two completely different things

https://www.physicsforums.com/library.php?do=view_item&itemid=27" is a linear acceleration, in m/s2,

but angular acceleration, in rad/s2, isn't

(these questions are usually about something starting from rest, and going through a given angle in a given time … in that case, you simply use the angular versions of the standard https://www.physicsforums.com/library.php?do=view_item&itemid=204" equations)

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My book says this:

Uniform Angular Acceleration
From Newton’s first law we know that an object moving in a circle must be acted upon
by a force causing it to continually change direction. Hence such an object must be
experiencing an acceleration. Just as we did for angular velocity, we will now derive an
expression for the angular acceleration.The first point to note is that the acceleration of an object moving in a circle is towards
the centre of the circle. Imagine a stone on a length of string being whirled around
your hand. Clearly, the force acting on the stone is supplied by the string and acts towards
the centre of the circle. The acceleration is in the same direction as the force, and can be
shown to be

V2
––
r

This formula gives the acceleration in metres per second2. (Test this by substituting units
into the equation.) To find the angular acceleration in radians per second2,
substitute for v from w = v/r
This yields:
Angular Acceleration = ω2r

Is all that a load of rubbish then?

Going back to angular velocity for one moment:

the formula i was given is w=theta/t

How do i apply that to get the answer?

i checked that formula with this http://eculator.com/formula/calculator.do?equation=Angular-Velocity&id=204
but i dont know what values to stick in the theta or time?

Thanks for your time and patience with this

I hate this course with a passion, not one word makes sense

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tiny-tim
Homework Helper
Hi Joe!
My book says this:

Uniform Angular Acceleration

From Newton’s first law we know that an object moving in a circle must be acted upon by a force causing it to continually change direction. Hence such an object must be experiencing an acceleration. Just as we did for angular velocity, we will now derive an expression for the angular acceleration.

The first point to note is that the acceleration of an object moving in a circle is towards the centre of the circle. Imagine a stone on a length of string being whirled around your hand. Clearly, the force acting on the stone is supplied by the string and acts towards the centre of the circle. The acceleration is in the same direction as the force, and can be shown to be

V2
––
r

This formula gives the acceleration in metres per second2. (Test this by substituting units into the equation.) To find the angular acceleration in radians per second2, substitute for v from w = v/r
This yields:
Angular Acceleration = ω2r
Is that from your www.icslearn.co.uk course?

That is rubbish. You should get your money back.

Where it says "Uniform Angular Acceleration" (I've put it in blue) is completely wrong, it should obviously be "Uniform Angular Velocity".

(as wukunlin said, the angular acceleration will be zero)

The other three times it says "angular acceleration" (in red) are also completely wrong, they should call it "https://www.physicsforums.com/library.php?do=view_item&itemid=27"".​

Apart from that, it is correct, but the way they've used the wrong expression is completely misleading.

Seriously, if you haven't done much of the course yet, point out this mistake to them and ask them to give you your money back, and threaten to take them to the Small Claims Court if they don't.
… the formula i was given is w=theta/t

but i dont know what values to stick in the theta or time?
θ (has to be in radians) is 2π (one revolution), and t is 3 (seconds).

EDIT: hmm … just noticed another mistake!

It says "The first point to note is that the acceleration of an object moving in a circle is towards the centre of the circle."

No, it should say "The first point to note is that the acceleration of an object moving uniformly in a circle is towards the centre of the circle."

(and the example about string being whirled around your hand is a bad example … unless the circle is vertical, the acceleration won't be along the string … and even if it is vertical, your hand won't be stationary, and it won't be a circle )​

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Yeah this is the ics course, i have pretty much finished the first assesment 1/3. The whole course is like this, mistakes from start to end, its winding me up considering maths never was a strong point and then for it not to be taught correctly is another thing.

What does n stand for again sorry?

Thanks again for all your help

tiny-tim
Homework Helper
What does n stand for again sorry?
oh, that's π (pi) !

(are you reading this on a phone?)​

pi? n's, now you have lost me completely haha

EDIT' so 2pi equals one revolution?

Im sick of this haha, ive spent the past 12 hours trying to understand one question and still no closer

tiny-tim
Homework Helper
EDIT' so 2pi equals one revolution?
YES!!

radians = 360° = one revolution

(check it on your calculator if you don't believe me! )

π = 180°

π/2 = 90°

You should learn these by heart, so that you know them instinctively!!

(and you should interpret the question as asking for the angular velocity and the centripetal acceleration)

Right i understand this finally. Many aggonising hours later and:

2π = 360 degrees takes three seconds to do this so divide by 3 = 2.094 rad/s

so basically the theta has to be in radians and it takes 3 seconds to complete a full revolution.

So this formula can be applied to any circle?

What a huge relief, many aggonising hours later and im getting somewhere.

This should mean that the w2r is also correct and has now finished my question.

Thankyou very much for your help, could not have done this without you, im sure ill be back very shortly with some mind boggling problems.

tiny-tim
Homework Helper
so basically the theta has to be in radians and it takes 3 seconds to complete a full revolution.

So this formula can be applied to any circle?
Yes, the theta has to be in radians, or the formula doesn't work!

(and yes, it applies to any circle )

Sorry to bump an old thread but I am completely stumped by this same question and cannot seem to work it out for love nor money!

I worked out the Velocity the same as the OP in his first post to 3.14

"1. Homework Statement
Calculate the angular acceleration and angular velocity of a 2kg object rotating in a
circle of 1.5m radius in a time of 3s.
2. Homework Equations
w=v/r
2*pie*r
3. The Attempt at a Solution

Now i dont know how to fully work this out, not sure how to apply the forumla.
3 seconds for one complete roatation
360 / 3 = 120 degrees
120 degrees per second
2*pie*r=
9.42m
9.42 / 3 = 3.14ms-1
I know this completes 120 degrees going a distance of 3.14m in a second."

I have taken this to be the final velocity, work work out the acceleration as above I am completely stumped by this question the course material has not helped at all :(

I need to get this done ASAP and this is really stressing me out now...

tiny-tim
Homework Helper
welcome to pf!

hi judderman! welcome to pf!

the difficulty with this question (i assume i'ts from the same ics course?) is that we don't know whether …
Calculate the angular acceleration and angular velocity …
means angular acceleration and angular velocity,

or means centripetal acceleration and tangential velocity (ie speed)

it appears to be the latter

ok, the tangential velocity is ωr

and the centripetal acceleration is ω2r (or v2/r … same thing)

does that help?

(btw, your calculation for ω would be quicker if you avoided degrees completely, just going from rpm to rps, and then converting from revolutions to radians by multiplying by 2π )

Hi, thanks for the reply and the welcome :)

It is an ICS learning course and frankly the material is terrible but its paid for now and I just need to motor on with it :(

Ok so assuming from what was said earlier in this thread that the latter is correct and its describing centripetal acceleration and tangential velocity (speed).

1) Is my original calculation for ω correct?
2) Tangential Velocity then = 3.14 x 1.5 = 4.71ms-2 ???
3) Centripetal Acceleration = 4.71^2 / 1.5 = 14.7894

Please for the love of the lord tell me this is finally right?

Thanks
Judd

tiny-tim
Homework Helper
Hi Judd!
Hi, thanks for the reply and the welcome :)

It is an ICS learning course and frankly the material is terrible but its paid for now and I just need to motor on with it :(

Ok so assuming from what was said earlier in this thread that the latter is correct and its describing centripetal acceleration and tangential velocity (speed).

1) Is my original calculation for ω correct?
Let's see …

one revolution in 3 s, so ω = 2π/3 (I'm using ω for the actual angular velocity, not the ICS version ),

so v (the tangential velocity, ie the ICS angular velocity) = ωr = 2π(1.5)/3 = π m/s
2) Tangential Velocity then = 3.14 x 1.5 = 4.71ms-2 ???
3) Centripetal Acceleration = 4.71^2 / 1.5 = 14.7894
No, you've completely lost the plot.

Unfortunately, the plot is written by ICS, in a language similar, but not identical, to English.

π m/s is the tangential velocity, usually written v = ωr

centripetal acceleration is v2/r, = ω2r

Haha, ICS has worn me down and is killing me inside... Time to start from scratch with this help :)

Thanks I'm travelling for the rest of the day now so will try this when I get in or tomorrow morning!

Really really appreciate the help :)

Ok i need to put out an SOS call on this. I to am doing the ICS course and spend 10 hours + trying to translate the ICS language (Not going to good). I'm attempting the same question here. Read this thread over and over again. In simple terms could someone please give me a reason to live and confirm i have the correct logic for the answer below.

To get θ i use the equation 2∏/time (answer given in rad/s)

Then i use my answer from this and subtitude it into ω2r (answer given in rad/s2) to get the acceleration?

tiny-tim
Homework Helper

## Homework Statement

Calculate the angular acceleration and angular velocity of a 2kg object rotating in a
circle of 1.5m radius in a time of 3s.
hi junkie_ball!
To get θ i use the equation 2∏/time (answer given in rad/s)
i assume you mean to get ω?

yes that's correct, ω = 2π/period
Then i use my answer from this and subtitude it into ω2r (answer given in rad/s2) to get the acceleration?
if it's ω2r, it can't be rad/s2, can it?

ω2r has dimensions length/time2, rad/s2 only has dimensions 1/time2

ω2r (= v2/r) is what normal people call the centripetal acceleration, it is an ordinary linear acceleration, measured in m/s2

what normal people call the angular acceleration is dω/dt (= d2θ/dt2), measured in rad/s2

however, ics doesn't use normal english …​

in a university exam, the question ("angular acceleration and angular velocity") will mean dω/dt and ω

in ics's little world, apparently it means ω2r and ωr

Hi mate,

I subbed my work last week, with the help of the guys on here!
Thanks especially to Tiny_Tim who is the master homework helper!!!

You need every answer to be correct to pass, I got 4 wrong and the paperwork will be on the way back if I have got it right I will share my method with you but obviously not disclosing the answers etc as you should be able to work it out with a little help :)

Tiny Tim Thanks for the break down i see i have my units of measure confused. Will have another look at it.

I have already confronted ICS with at least four errors in their course work. The tutor replies it's an error in the text and my workings seems to be right and they will look at it. That's all you get. I wish i could have found another home study course for mechanical engineering as unable to fit college in with my current job so having to make do with this ICS one.

Judderman.

I really appreciate that and good to know i'm not the only one suffering on this course. I will add you as a contact on here and perhaps we could share notes for further parts of the course and help each other out.

tiny-tim