Rotational Kinematics -- questions about a=mg sin(theta) / (m+I/R^2)

  • #1
MP97
4
0
Hi, I am learning. Rotational Kinematics and I was given this formula in class: a=mgsin(theta)/(m+I/R^2); however, I couldn't understand the professor's explanation of where it comes from. Could someone provide some insights about it?

I appreciate any help you can provide.
 
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  • #2
Do you at least have an idea of what physical situation it is supposed to describe? Is the formula you posted all there is in your notes? It looks like you have a mass sliding down a frictionless incline of angle ##\theta##. A massless string is tied to the mass and wrapped around a pulley of radius ##R## and moment of inertia ##I##. The expression you posted describes the linear acceleration of the mass down the incline.

It comes from the application of Newton's second law for linear motion and for rotations. If you want to see its derivation, I am sure you can find it on the web now that you know what it (probably) is.
 
  • #3
Correct it describes an object rolling down an inclined plane without slipping. Thank you!
 
  • #4
MP97 said:
Correct it describes an object rolling down an inclined plane without slipping. Thank you!
That's not what I said, but it describes that too. You are welcome.
 
  • #5
MP97 said:
Hi, I am learning. Rotational Kinematics and I was given this formula in class: a=mgsin(theta)/(m+I/R^2); however, I couldn't understand the professor's explanation of where it comes from. Could someone provide some insights about it?

I appreciate any help you can provide.
For some insights, you could try this:

 

What is the formula for rotational acceleration (a) in terms of gravity (g), angle (theta), moment of inertia (I), and radius (R)?

The formula for rotational acceleration is a = mg sin(theta) / (m + I/R^2), where m is the mass, g is the acceleration due to gravity, theta is the angle, I is the moment of inertia, and R is the radius.

How does the rotational acceleration formula differ from linear acceleration?

The rotational acceleration formula takes into account the moment of inertia and radius, which are specific to rotational motion, while linear acceleration only considers mass and force.

What is the significance of the term I/R^2 in the rotational acceleration formula?

The term I/R^2 in the formula represents the rotational inertia of the object relative to its radius. It accounts for how the distribution of mass affects the rotational acceleration of the object.

Can the rotational acceleration formula be used for objects in uniform circular motion?

Yes, the rotational acceleration formula can be used for objects in uniform circular motion, as it describes the acceleration experienced by an object rotating about a fixed axis.

How can the rotational acceleration formula be applied in real-world scenarios?

The rotational acceleration formula can be used to calculate the acceleration of objects undergoing rotational motion, such as wheels, gears, and rotating machinery. It is essential for understanding the dynamics of rotating systems and designing efficient mechanisms.

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