Kinematics of Rigid Body Plane Motion

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Homework Help Overview

The discussion revolves around the kinematics of a rigid body, specifically a wheel rotating about a fixed axis. The problem involves determining the absolute acceleration of point C on the wheel, given the velocities of points A and B, and the radius of the wheel.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between the velocities and accelerations of points A, B, and C, questioning how these relate to each other. There are attempts to express tangential and normal accelerations in vector form, and discussions about the angles involved in these vectors.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning each other's reasoning. Some guidance has been offered regarding the relationships between the points' velocities and accelerations, and there is a focus on ensuring clarity in vector representation.

Contextual Notes

Participants are working within the constraints of the problem as stated, referencing specific equations related to rigid body motion. There is an emphasis on understanding the components of acceleration and the geometry involved in the setup.

  • #31
TSny said:
Speed doesn't have a direction.
This is just not making sense to me.
 
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  • #32
Speed is the magnitude of the velocity. Velocity is a vector. Speed is a scalar.

So, the velocity of C is not the same as the velocity of A. But the speed of C does equal the speed of A.
 
  • #33
TSny said:
Speed is the magnitude of the velocity. Velocity is a vector. Speed is a scalar.

So, the velocity of C is not the same as the velocity of A. But the speed of C does equal the speed of A.
but you can't get acceleration from speed
 
  • #34
You can get the magnitude of the normal acceleration from the speed and the radius. Normal acceleration is also called centripetal acceleration.
 
  • #35
TSny said:
You can get the magnitude of the normal acceleration from the speed and the radius. Normal acceleration is also called centripetal acceleration.
how would you find the angular acceleration and velocity of the wheel?
 
  • #36
Are you familiar with the formula acentripetal = v2/r ?

Or are you required to solve this problem using only the equations that you listed:

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
 
  • #37
TSny said:
Are you familiar with the formula acentripetal = v2/r ?

Or are you required to solve this problem using only the equations that you listed:
Yes I am familiar with such equation
 
  • #38
Great! What do you get for the magnitude of the centripetal acceleration?
 
  • #39
TSny said:
Great! What do you get for the magnitude of the centripetal acceleration?
49/6
 
  • #40
√(49)/6
Why the square root?
 
Last edited:
  • #41
TSny said:
Why the square root?
brain fart just 49/6
 
  • #42
OK. All you need to do is put it all together now.
 
  • #43
TSny said:
OK. All you need to do is put it all together now.
the magnitude of the normal acceleration would be radius times angular acceleration which we know from point B correct?
 
  • #44
Yes, but why go there? You already have values for an and at. Use these in your earlier expressions to obtain the normal and tangential acceleration vectors in terms of i and j. For example, see your post #21.
 
  • #45
TSny said:
Yes, but why go there? You already have values for an and at. Use these in your earlier expressions to obtain the normal and tangential acceleration vectors in terms of i and j. For example, see your post #21.
But what is the value of an
 
  • #46
Post # 41 ??
 
  • #47
no no sorry at
 
  • #48
How does the magnitude of the tangential acceleration of C compare to the magnitude of the tangential acceleration of B?
 
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  • #49
TSny said:
How does the magnitude of the tangential acceleration of C compare to the magnitude of the tangential acceleration of B?
SAME
 
  • #50
Yes.
 
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  • #51
TSny said:
Yes.
When I plug and chug I do not get the answer :/
 
  • #52
What numerical values did you get for the x and y components of ##\vec{a}_t##?

What numerical values did you get for the x and y components of ##\vec{a}_n##?
 
  • #53
Nevermind...got it finally. Thank you so much for your continued help. I am extremely grateful!
 
  • #54
OK. Good work.
 
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