Acceleration of center of mass

• Ian Blankenship
In summary, the question is asking for the representation of linear acceleration of the center of mass of link OA, given certain variables and equations. The problem becomes simple if the weight of the rod is the only force acting on it, but there may be other forces at play. However, considering that the angular velocity of OA is fixed and point O is fixed, the motion of all points on OA can be determined without considering forces. This results in a tangential acceleration of zero for all points, but the linear acceleration of the center of mass may not necessarily be zero.

Homework Statement

"Represent (linear) acceleration of center of mass of link OA in terms of variables shown." OmegaOA is given to be some constant value, I have assigned it 'omegaOA'.

Homework Equations

Already derived equations to previous parts of the problem, fairly certain these are correct. Relative variables are neglected, since this is a single body problem. 'a' is linear acceleration, alpha is angular acceleration.
omegaAB = (omegaOA*b*cos(theta))/sqrt(d^2 - (b*sin(theta) + h)^2)
alphaOA = 0
alphaAB = [-(omegaOA^2)*b*sin(theta) - (omegaAB^2)*(b*sin(theta)+h)]/sqrt(d^2 + (b*sin(theta) + h)^2)
alphaOA = (a/r)

The Attempt at a Solution

If the weight (mg) of the rod was the only force acting on the rod, the problem is very simple.

I*alpha = torque where I = (1/12)*m*length^2
Mass cancels and the problem is easy to solve. However, I am guessing there are force vectors at A that need to be taken into account. Any help would be appreciated.

Attachments

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haruspex said:
If the angular velocity of OA is fixed, and point O is fixed, how does anything to the right of A affect the movement of OA? Are you sure you have stated the question correctly?
And why did you mark the previous thread https://www.physicsforums.com/threads/acceleration-of-center-of-mass.912120/ as solved, then open a new one for the same question?
Sorry about the repost, I had stated the problem poorly the first time, so I figured it would save the time of those replying to make a more precise and accurate post of the question.
And the 'relevant equations' that I have listed are just there because I'm trying to give as much info as possible. And if the reaction forces at A are worked around, there are still support forces at O (according to my analysis, could be wrong). I.e. a simple moment analysis appears to lead to a confusing situation, with either forces at A or O coming up

Ian Blankenship said:
if the reaction forces at A are worked around,
Why do you care about forces at all? Point O is fixed, the rotation rate of OA is fixed. That tells you everything about the motion of all points on OA.

That makes sense..so the linear acceleration of the center of mass would be zero? I would assume that all points along the link OA would have an acceleration of zero.

Ian Blankenship said:
so the linear acceleration of the center of mass would be zero?
No. It has a tangential acceleration of zero.
Linear acceleration of a point is its total acceleration, tangential plus radial (vectorially). Linear acceleration of a rigid body is the linear acceleration of its mass centre.

What is acceleration of center of mass?

Acceleration of center of mass is a measure of how quickly the center of mass of an object changes its velocity over time. It is a vector quantity that takes into account both the magnitude and direction of the object's motion.

How is acceleration of center of mass calculated?

Acceleration of center of mass is calculated by taking the derivative of the velocity of the center of mass with respect to time. This can be done using the formula a = Δv/Δt, where a represents acceleration, Δv represents the change in velocity, and Δt represents the change in time.

What factors affect the acceleration of center of mass?

The acceleration of center of mass is affected by several factors including the mass of the object, the force acting on the object, and the distribution of mass within the object. The acceleration can also be affected by external forces, such as friction or air resistance.

Why is the concept of acceleration of center of mass important in physics?

The concept of acceleration of center of mass is important in physics because it allows us to analyze the motion of complex systems, such as multiple objects moving together, as if they were a single object. This simplifies calculations and helps us understand the overall motion of the system.

How does acceleration of center of mass relate to Newton's laws of motion?

Acceleration of center of mass is closely related to Newton's laws of motion. According to Newton's second law, the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. Since center of mass takes into account the mass and motion of the entire object, it allows us to apply this law to the object as a whole.