Kinematics of Rigid Body Plane Motion

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SUMMARY

The discussion focuses on the kinematics of rigid body plane motion, specifically analyzing the absolute acceleration of Point C on a rotating wheel with a radius of 6 inches. The velocities of Points A and B are given as -7j in/sec and -4i in/sec², respectively. The participants conclude that the absolute speed of Point C equals that of Point A, while the tangential acceleration of Point C is expressed in terms of unit vectors, with the normal acceleration directed towards the center of the circle. The discussion emphasizes the importance of understanding both tangential and normal components of acceleration in rigid body motion.

PREREQUISITES
  • Understanding of rigid body dynamics
  • Familiarity with angular velocity and angular acceleration
  • Knowledge of vector decomposition in physics
  • Proficiency in using kinematic equations for rotational motion
NEXT STEPS
  • Study the derivation of the centripetal acceleration formula: acentripetal = v²/r
  • Explore the relationship between angular velocity and linear velocity in rigid body motion
  • Learn how to decompose acceleration vectors into tangential and normal components
  • Practice problems involving the kinematics of rotating bodies using equations of motion
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Students and professionals in mechanical engineering, physics, and applied mathematics who are studying the dynamics of rigid bodies and analyzing rotational motion.

  • #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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