# Calculate the angular acceleration and angular velocity

1. ### joe465

94
1. The problem statement, all variables and given/known data

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. Relevant 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.

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

2. ### wukunlin

388
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:

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

3. ### joe465

94
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

4. ### wukunlin

388
from what I'm seeing you are on the right track, it just feels like the questions has some irrelevant data and vague information

5. ### joe465

94
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

Last edited: Aug 28, 2011
6. ### joe465

94
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

7. ### tiny-tim

26,053
Hi Joe!

(have a pi: π and an omega: ω )
no wukunlin is right, and centripetal acceleration and angular acceleration are two completely different things

centripetal acceleration 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 constant acceleration equations)

8. ### joe465

94
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

Last edited: Aug 28, 2011
9. ### tiny-tim

26,053
Hi Joe!
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 "centripetal acceleration".​

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.
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 )​

Last edited: Aug 28, 2011
10. ### joe465

94
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

11. ### tiny-tim

26,053
oh, that's π (pi) !

(are you reading this on a phone?)​

12. ### joe465

94
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

13. ### tiny-tim

26,053
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)

14. ### joe465

94
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.

15. ### tiny-tim

26,053
Yes, the theta has to be in radians, or the formula doesn't work!

(and yes, it applies to any circle )

16. ### judderman

5
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. The problem statement, all variables and given/known data
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. Relevant 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...

17. ### tiny-tim

26,053
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 …
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 )

18. ### judderman

5
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

19. ### tiny-tim

26,053
Hi Judd!
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
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

20. ### judderman

5
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 :)