Idea of Rolling, Rotation, and Transition

In summary, the conversation discusses the application of Newton's laws of forces and torques on rolling bodies. The book explains that rolling can be separated into pure translation and pure rotation, but there is confusion about calculating forces on pure translation and how it affects kinetic energy. The speaker believes that forces not applied through the center of mass will create both rotational and translational kinetic energy, but the book only uses the full magnitude of forces for Newton's 2nd law in rolling motion. It is important to understand that the point of application of a force does not affect the acceleration of the center of mass, but it does impact the work done and overall kinetic energy of the object.
  • #1
Biloon
6
0
I'm very confuse about the idea of applying Newton's law of forces and torques on rolling body. The book shows that you can separate the situation in rolling into pure transition and pure rotation. However, what I don't get is, for the calculation of Newton's 2nd law of forces on pure transition, they calculate all forces, not just the one through center of mass... If what I remembered, the forces that are not through center of mass should create both rotational and transitional kinetic energy, right? In case of rolling, the 2nd law simply applied as sigma F = ma, where F is applied anywhere on the body.

From that equation, I got myself into some contradiction. In case 1, If i have a Force F applied on the center of mass, then it accelerates with F = ma. In case 2, if the force is not directed on the center of mass, and if I follow the book, the book simply use Newton 2nd law of forces and torques... so my accelerations remain the same but with some extra torque. Therefore, for the same amount of force and over certain period of time, both cases will not have the same kinetic energy...

From what I believe, the force that is not on the center of mass will be distribute into rotational and transitional kinetic energy. However, the book simply applied full magnitude of forces not through center of mass for Newton 2nd law in rolling motion; that is really disturbing for me.
 
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  • #2
Don't confuse the application of Newton's 2nd law (ΣF = ma) with the work done by the applied force. As far as Newton's 2nd law goes, the point of application of the force doesn't matter when calculating the acceleration of the center of mass. But it certainly does when calculating the work done by the force.

If you apply the force off-center (so it exerts a torque about the center of mass) then the point of application of the force will move through a greater distance, which requires more work done and thus ends up giving the object more overall kinetic energy. The translational KE of the center of mass doesn't change but the rotational KE does--the 'extra' work goes into rotational KE.
 

FAQ: Idea of Rolling, Rotation, and Transition

1. What is the difference between rolling, rotation, and transition?

Rolling is the movement of an object along a surface without slipping. Rotation is the spinning of an object around a fixed axis. Transition is the change from one state or position to another.

2. How are rolling, rotation, and transition related?

Rolling and rotation are both types of motion, with rolling being a combination of rotation and translation (linear motion). Transition can occur during rolling or rotation, as an object can transition from one state of motion to another.

3. What are some real-life examples of rolling, rotation, and transition?

Rolling: a ball rolling down a hill, a car moving on a road. Rotation: a spinning top, a rotating fan. Transition: a door opening and closing, a pendulum swinging back and forth.

4. How do rolling, rotation, and transition affect objects differently?

Rolling can be more efficient for movement than sliding, as it requires less force to maintain motion. Rotation can change an object's orientation or direction of movement. Transition can cause an object to change its position, speed, or direction of motion.

5. What are some important concepts to understand about rolling, rotation, and transition?

Some important concepts include the conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque. The law of inertia also applies to rotation, stating that an object will maintain its state of rotation unless acted upon by an external torque. Understanding the relationship between these concepts can help explain the behavior of rolling, rotation, and transition in various scenarios.

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