Rotational kinematics check please.

[pat666]

Homework Statement

4. An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s².
a) Compute the angular velocity of the turntable after 0.200s my answer:1.35rev/s
b) Through how many revolutions has the turntable spun in this time interval? my answer:0.01
c) What is the tangential speed of a point on the rim of the turntable at t = 0.200 s? my answer: 0.51
d) What is the magnitude of the resultant acceleration of a point on the rim at t = 0.200 s?
my answer: 6.9 rev/s^s really unsure of this one.

Homework Equations

The Attempt at a Solution

for d:
I found the angular acceleration (alpha) to be 5.5 then using the relationship alpha =a/r to find the translational acceleration. From there i used Pythagoras' theorem to solve for the resultant. I know I've been asking for a lot of checking of my work lately, just because i am not great with the topics were doing this term. I do always have a good attempt at the problem before asking for help. thanks in advance.

 

[Squeezebox]

Angular acceleration is constant. How did you end up with the 5.5 value?

 

[pat666]

There's one problem i think that i found the angular velocity at 0.2s, do you know if the rest is right?

 

[pat666]

sorry i got it by doing alpha=(w0-w)t, why is that wrong or is my tangential acceleration meant to be 0.9?

 

[Squeezebox]

B is right, the rest are wrong.

 

[pat666]

well that's not good news for me. why is the first one wrong. I just found this which agrees with me about most of them except the last one, can you please take a look. http://www.cramster.com/answers-nov-09/physics/helpppp-pleaseee-an-electric-turntable-0750-m-in-diameter-is-rotating-about_703471.aspx

Could you please help me fix them if thay are wrong i really have no idea where i could be wrong for the first few??

 

[Squeezebox]

I don't think you're calculating them correctly because they agree with the values I got which do not agree with your values.

 

[pat666]

Im an idiot is the problem, my physics is correct i think but my maths is not, is your answer for a) 0.43rev/s?, for c) 0.16125m/s and could you give me a hand for d please. thanks

 

[ehild]

pat666, always fill in the template and show your full work. It is easier to check what you did wrong and what is only computational mistake.
What is the equation you used to get the angular acceleration in rad/s^2 from 0.900 rev/s^2?

Just a hint: Trust in yourself and in your Physics textbook and teacher. Do not believe anything that you find on the Net.

ehild

 

[pat666]

Hey ehild, how do i get an equation to display properly here, i know its hard to read and I've seen people post equations that look like equations but i can't get it to work: I am an idiot is the problem, my physics is correct i think but my maths is not, is your answer for a) 0.43rev/s?, for c) 0.16125m/s and could you give me a hand for d please. just repeated my last post since we posted at exactly the same time.

 

[Squeezebox]

Hey ehild, how do i get an equation to display properly here, i know its hard to read and I've seen people post equations that look like equations but i can't get it to work: I am an idiot is the problem, my physics is correct i think but my maths is not, is your answer for a) 0.43rev/s?, for c) 0.16125m/s and could you give me a hand for d please. just repeated my last post since we posted at exactly the same time.

Yea those are the answers I got as well.

Resultant vector depends on the tangential and centripetal accelerations.

 

[pat666]

centripetal acceleration would be 0.9? and tangential would be 0.9*r?

 

[Squeezebox]

centripetal acceleration would be 0.9? and tangential would be 0.9*r?

No, angular acceleration is 0.9 rad/s².

a_c=v_t²/r

a_t=\alphar

 

[ehild]

People use tex to write the equations in nice form, see the thread Introductory Physics Formulary. But you can simply use symbols +,-,*,/ ^, and write out Greek letters and functions, it will do either.

As for angular speed, the SI unit is rad/s, and rev/s is rather called rotational speed. The relation between tangential speed and angular speed, v=r*w or the relation between tangential acceleration and angular acceleration a = r*alpha is valid only in the rad/s, rad/ s^2 units.

ehild

 

[pat666]

Hey, did you get a_c=0.0693 and a_t=0.3375 and the resultant = 0.34?

 

[ehild]

No, angular acceleration is 0.9 rad/s².

Look at the original post: angular acceleration is 0.9 rev/s^2.

ehild

 

[ehild]

Hey, did you get a_c=0.0693 and a_t=0.3375 and the resultant = 0.34?

Write out the units.

ehild

 

[pat666]

OK, ill also tell you what i did. I have angular acceleration as 0.9rev/s^2 so i stuck that in a_t=alpha*r and got 0.3375m/s^2,,,,,,,, angular acceleration is alpha isn't it? For the centripetal acceleration i did a_c=〖0.16〗^2/0.375 from that i got a_c=0.07rev/s^2 that is v_t^2/r... sorry about the units I am drawing a blank on them. I thought that tangential acceleration had units of m/s^2 and centripetal acceleration had units of rev/s^2, but reading back over what you have said i take it that that is not right?

 

[pat666]

Does the acceleration have to be in rad/s if it does i would just times it by 2pi wouldn't i??

 

[ehild]

a_t= alpha * r is valid if you measure the angular speed in rad/s. rad has de dimension of "1": the angle in radians is the arc length divided by the radius. So you have to convert angular velocity to rad/s unit before you calculate tangential velocity.
In your first post in this thread you said the angular acceleration was 5.5 (without units) Well, it is 0.9 (rev/s) * 2 pi (rad/rev) = 5.65 rad/s^2.

Your present values for the components of linear acceleration are wrong.


ehild

 

[ehild]

Does the acceleration have to be in rad/s if it does i would just times it by 2pi wouldn't i??

The angular acceleration has to be in rad/s^2. .

ehild

 

[pat666]

Ok ill go back and do everything in rad/s^2 which will change all of my values i think. ill soon see anyway. ill post my new results up when i do them.

 

[pat666]

Ok I've done them
a) ω=1.38rad/s
b)0.256revolutions
c)v=0.518rev/s should this be m/s??
d)4.86rad/s^s not sure on the units for the resultant.
Can you please check these. thanks!

 

[ehild]

Ok ill go back and do everything in rad/s^2 which will change all of my values i think. ill soon see anyway. ill post my new results up when i do them.

You do not need to change everything. And do not forget to write out the formula you use.
So again: how do you get rad/s from revolution/s ?

ehild

 

[pat666]

multiply by 2pi that's what i did anyway, but i like to keep all the units consistent in a problem that's why i moved all of my solutions to si units(i hope not sure on a few units), so are the values i gave correct?

a) ω=1.38rad/s
from ω=ω_0+αt
ω=0.250+5.56*0.2

b)0.256revolutions
from θ=ω_0 t+1/2 αt^2 then n=theta/2pi
c)v=0.518rev/s should this be m/s??
from v=rω
d)4.86rad/s^s not sure on the units for the resultant.
from what I've been told on this thread.

 

[Squeezebox]

multiply by 2pi that's what i did anyway, but i like to keep all the units consistent in a problem that's why i moved all of my solutions to si units(i hope not sure on a few units), so are the values i gave correct?

a) ω=1.38rad/s
from ω=ω_0+αt
ω=0.250+5.56*0.2

b)0.256revolutions
from θ=ω_0 t+1/2 αt^2 then n=theta/2pi
c)v=0.518rev/s should this be m/s??
from v=rω
d)4.86rad/s^s not sure on the units for the resultant.
from what I've been told on this thread.

a) You didn't convert the units of ω₀.
b) Wrong for same reason as a.
c) Wrong for same reason as a.
d) Can you show the calculation?

You know what your doing, just didn't convert.

 

[pat666]

orrrrrrrrrrrrrrrr that's what yous have been trying to tell me, sorry completely missed that.

 

[pat666]

a) ω=2.68rad/s
b) 0.10revolutions
c) v=1.0rev/s or m/s?
d) a_c=(v_t^2)/r
a_c=1^2/0.375
a_c=2.67

a_t=α*r
a_t=5.56*0.375
a_t=2.085

then sqrt(2.67^2+2.085^2) =3.39rad/s^2 or m/s^2??

 

[Squeezebox]

a) ω=2.68rad/s
b) 0.10revolutions
c) v=1.0rev/s or m/s?
d) a_c=(v_t^2)/r
a_c=1^2/0.375
a_c=2.67

a_t=α*r
a_t=5.56*0.375
a_t=2.085

then sqrt(2.67^2+2.085^2) =3.39rad/s^2 or m/s^2??

a) correct
b) still incorrect
c) correct, m/s (rads are kind of like a place holder unit in this case so it goes away, i don't know the actual reason why though)
d) correct, m/s² (for same reason)

 

[pat666]

so can you tell me what you got for b, do you think that it is just a computational area.

 

[Squeezebox]

θ=ω_0 t+1/2 αt^2 then n=theta/2pi

θ=0.5*pi*0.2+.5*1.8*pi*.04=pi(0.1+0.036)=0.136*pi

θ/2*pi=0.136*pi/2*pi=0.136/2=0.068 rev

 

[pat666]

Hey, i now have what you have, i subbed w at .2s in instead of w_0. thanks for all of your help.