# Kinematics of Rigid Body Plane Motion

1. Jul 18, 2016

### Auburn2017

1. The problem statement, all variables and given/known data
The wheel shown rotates about point O.
Point A has a velocity=-7j in/sec.
Point B has a tangential velocity=-4i in/sec^2
Determine the absolute acceleration of Point C located on the circle.
You will have to look at the figure for more clarification please.
2. Relevant equations
rA=rB+rA/B
vA=vB+vA/B
aA=aB+aA/B
vA/B=ω×rA/B
aA/B=(aA/B)n+(aA/B)t
(aA/B)n=ω×(ω×rA/B)
(aA/B)t=α×rA/B
3. The attempt at a solution
I tried finding the velocity of C relative to A. I feel like there is an easy way to find the angular acceleration and angular velocity of the wheel but I dont really know how. Thanks for your help.

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2. Jul 18, 2016

### TSny

The wheel is considered to be a rigid body rotating about a fixed axis. How does the absolute speed of point C compare to the absolute speed of A? How does the magnitude of the absolute tangential acceleration of C compare to that of B?

Last edited: Jul 18, 2016
3. Jul 18, 2016

### Auburn2017

Since all three points are on the edge of the wheel then they should all have the same absolute acceleration and velocity.

4. Jul 18, 2016

### TSny

The magnitudes of the velocity and tangential acceleration will be the same. Directions?

5. Jul 18, 2016

### Auburn2017

velocity CW
acceleration CCW

6. Jul 18, 2016

### TSny

OK. But more specifically, can you express the tangential acceleration vector of point C in terms of the unit vectors $\hat{i}$ and $\hat{j}$?

7. Jul 18, 2016

### Auburn2017

No I can't. Isn't that what the problem is asking?

8. Jul 18, 2016

### TSny

No, there's more to the problem than just doing that. Does point C have any other component of acceleration besides tangential?

9. Jul 18, 2016

### Auburn2017

Yes it has a normal acceleration toward the center of the circle. I guess the tangential acceleration would be atcos60° i and atsin60° j

10. Jul 18, 2016

### TSny

You need to draw the tangential and normal acceleration vectors for point C on your diagram. The tangential acceleration of C is not vertically upward (i.e., not +j) and it's not "to the right" (i.e., not i).

11. Jul 18, 2016

### Auburn2017

12. Jul 18, 2016

### TSny

That's getting close. But you need to check if 60o is correct here.

13. Jul 18, 2016

### Auburn2017

yes it is correct

14. Jul 18, 2016

### TSny

Did you actually draw the tangential acceleration vector at C on your diagram? What angle does it make to the horizontal?

15. Jul 18, 2016

### Auburn2017

Yes I drew it. I'm not sure how to tell the angle though...

16. Jul 18, 2016

### TSny

You'll need to use a little geometry.

17. Jul 18, 2016

### Auburn2017

I'm going with 30 degrees

18. Jul 18, 2016

### TSny

Did you work it out, or is that a guess?

Look at the figure below. What is the angle $\phi$? Form $\phi$ do you see how to get $\theta$?

19. Jul 18, 2016

### Auburn2017

Yes theta would equal 30 degrees

20. Jul 18, 2016

### TSny

Good. Repeat for the normal acceleration.