Homework Help: Velocity and Acceleration Vectors

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1. Jan 23, 2016

CGI

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

2. Relevant equations
Rotational Kinematic Equations
Kinematic Equations

3. The attempt at a solution
I honestly have no clue how to get a vector out of this.

Θ = Θ(initial) + ω(initial)*t + .5αt^2

and how maybe that v = wr could play into this, but there is so much I don't know where to start.

Any help would be really appreciated!

2. Jan 23, 2016

TSny

3. Jan 23, 2016

CGI

Oh okay, so I should be thinking of something along those lines.

So if my theta = 0 and my R = .8ft, would my position vector just be r = .8êr?
what would my r dot and theta dot be? Sorry, this is still relatively new to me
and I've been watching videos on it as well. I just want to make sure I understand
this.

4. Jan 23, 2016

haruspex

Assuming the answers are wanted in terms of the x, y coordinates:
Let the diagram position represent time 0. At time t, what will r and theta be? So what will x and y be?

5. Jan 23, 2016

CGI

Would the x just be rcosΘ and y be rsinΘ?

6. Jan 23, 2016

haruspex

Yes, but you are trying to find velocities and accelerations, so you need to express them as functions of time.

7. Jan 23, 2016

CGI

Oh okay. Right. Could that just be rcostheta(t) and rsintheta(t)?

8. Jan 23, 2016

haruspex

According to the problem statement, both r and theta vary with time. Write each as a function of t.

9. Jan 23, 2016

CGI

Hmmm...okay. Could I say that r = r_initial + vt and that theta = theta_inital + wt where w = 45 rev/min?

10. Jan 23, 2016

haruspex

Yes. Now express x and y that way and differentiate as necessary.

11. Jan 23, 2016

CGI

When you say express x and y in that way, do you mean that I can say

x = (r_initial + vt)cos(Θ_initial + ωt)

And the same for y, only with a "sin?"

12. Jan 24, 2016

haruspex

Yes. Now differentiate.

13. Jan 24, 2016

CGI

Okay I was just double checking. So when I take the derivative with respect to t I get,

x = vcos(Θ_inital + ωt) - (r_initial + vt)sin(Θ_initial + ωt)*ω

y = vsin(Θ_inital + ωt) + (r_inital + vt)cos(Θ_initial + ωt)*ω

14. Jan 24, 2016

haruspex

Yes.

15. Jan 24, 2016

CGI

Okay great. So would these two x and y be the vector for velocity?

16. Jan 24, 2016

haruspex

Small correction: in your post #13 I presume you meant $\dot x=$ etc., not x=. Similarly y.
If so, yes they would be the x and y components of velocity.