Relative Velocity, Rigid Body Kinematics

[allyfranken]

Homework Statement

W(oa) = -5k
α(oa) = 3k
B = 30 deg
B(dot) = -2cos 30i + 2sin30j = Vrel
b(double dot) = 4cos30i - 4sin30j)

Homework Equations

Va = Woa x Rao + Vrel

The Attempt at a Solution

This is such a simple problem and I don't know why I am messing it up. I am just trying to figure out the Va part right now. I know the answer from the back is 4.38i + 7.58j

I did Va = W(oa) x R(ao) + Vrel solving for Va.
Va = -5k x 1.25(-cos30i + sin30j) + (-2cos 30i + 2sin30j)
Va = 3.125i + 5.4j - 1.73i - 1j

Va = 1.395i - 4.4j

This is what I am getting for Va but the answer is wrong. Can anyone point me in the right direction please?

 

[Simon Bridge]

Please you explain your reasoning at each step?

So - by "absolute velocity" the mean the linear velocity.
What does the rotation of the disk have to do with the motion of the sphere? Are the beta figures supposed to be wrt the rotating frome of the disk?

In your equations you appear to be making angular velocity and angular acceleration equal to linear velocity and acceleration. What is the relationship between angular velocity and tangential velocity?

Note: sin(30°)=1/2, cos(30°)=(√3)/2

 

[allyfranken]

yes by absolute velocity i mean linear velocity.

well I know that if point A was fixed, than Va = Woa x Rao. But since it is moving, Va = Woa x Rao + Vrel. I assume that Vrel is tangent to point A in the direction: 1.255i + 2.18j. and yes angular velocity is clockwise.

 

[Simon Bridge]

Please answer all the questions.

Did you mix up the sin and cos?
Consider, an object on a circular path 5" from the center, angular velocity 3rad/s clockwise, has a tangential velocity 15in/s right? When the angle is position 30deg anticlockwise from the horizontal, the velocity vector makes an angle of 60 degrees clockwise from the horizontal. sin(60)=cos(30).
(draw the pic)

hence: v= [-15sin(30)i+15cos(30)j]in/s = [-(7.5)i+(7.5√3)j]in/s
note: always include the units and you don't have to expand the √3 as 1.7321 until the very end.

 

[paranormal]

Dear student,

It appears that you have made a mistake in your calculation for Va. The correct calculation should be:

Va = -5k x 1.25(-cos30i + sin30j) + (-2cos 30i + 2sin30j)

= -6.25cos30j + 6.25sin30i + (-2cos30i + 2sin30j)

= -2.5j + 3.125i - cos30i + sin30j

= 1.125i - 2.5j

Therefore, the correct answer for Va is 1.125i - 2.5j, which is different from your previous calculation. Make sure to double check your calculations and equations to avoid any mistakes in the future. Keep up the good work!