# Calculate the angular acceleration and angular velocity

by joe465
Tags: acceleration, angular, velocity
 P: 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?
 PF Gold P: 340 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: $$a = \frac{v^2}{r}$$
 P: 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
PF Gold
P: 340

## Calculate the angular acceleration and angular velocity

from what I'm seeing you are on the right track, it just feels like the questions has some irrelevant data and vague information
 P: 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) 2.094 rad/s does this sound right? I dont have a clue what im doing to be honest
 P: 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
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P: 26,167
Hi Joe!

(have a pi: π and an omega: ω )
 Quote by joe465 Calculate the angular acceleration and angular velocity of a 2kg object rotating in a circle of 1.5m radius in a time of 3s.
 Quote by wukunlin do you mean angular acceleration or centripedal accleration? what you are using assumes constant angular velocity and angular acceleration is just zero …
 Quote by joe465 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

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)
 P: 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/calculat...elocity&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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P: 26,167
Hi Joe!
 Quote by joe465 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 "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.
 … 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 )
 P: 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
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P: 26,167
 Quote by joe465 What does n stand for again sorry?
oh, that's π (pi) !
(are you reading this on a phone?)
 P: 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
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P: 26,167
 Quote by joe465 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)
 P: 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.
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P: 26,167
 Quote by joe465 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 )
 P: 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...
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P: 26,167
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 …
 Quote by judderman 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 )
 P: 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

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