Force acting on the center of mass of a rolling disk

In summary, the conversation discusses the situation of a uniform disk being pulled by a string attached to its highest point, resulting in a force and acceleration on the center of mass. The moment of inertia and torque are mentioned, along with the relationship between torque and angular momentum. The conclusion is that the force acting on the body is equal to 2F divided by the mass of the disk, and the acceleration of the center of mass is equal to 2F divided by the mass of the disk multiplied by the radius. The question of whether the disk is rolling without slipping is also raised.
  • #1
Fibo112
149
3
Hello. The following situation I thought out confuses me so I am wondering where my mistake lies.
A uniform disk of mass M and radius R sits on its edge. A string is attached to the highest point and pulled with a Force F in the x direction.

The moment of inertia of the disk is MR^2/2 making the angular momentum about the center of mass MR^2w/2 where w is the angular velocity. The torque about the center of mass seems to be FR. Since torque is the derivative of angular momentum we have FR=MR^2a/2 where a is the angular acceleration.
This means the angular acceleration is equal to 2F/RM. The acceleration A of the c.o.m is equal to aR, so it is equal to 2F/M, making the force acting on the body equal to 2F/M*M= 2F?
 
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  • #2
Fibo112 said:
This means the angular acceleration is equal to 2F/RM. The acceleration A of the c.o.m is equal to aR
What makes you say that the acceleration of the center of mass is equal to aR? Nobody said that the disk was rolling without slipping.
 

1. What is the definition of center of mass?

The center of mass of an object is the point at which the entire mass of the object is considered to be concentrated. For a uniform object, the center of mass is located at the geometric center of the object.

2. How is the center of mass of a rolling disk different from that of a stationary disk?

The center of mass of a rolling disk remains the same regardless of its motion. However, the center of mass of a stationary disk is fixed at the geometric center of the disk.

3. What is the relationship between force and center of mass for a rolling disk?

For a rolling disk, the force acting on the center of mass is directly proportional to the acceleration of the disk. This is described by Newton's second law of motion, F=ma.

4. How does the shape of a rolling disk affect the force acting on its center of mass?

The shape of a rolling disk does not affect the force acting on its center of mass. However, the distribution of mass within the disk can affect the rotational motion of the disk.

5. Can the force acting on the center of mass of a rolling disk change during its motion?

Yes, the force acting on the center of mass of a rolling disk can change if an external force is applied to the disk or if there is a change in the distribution of mass within the disk. However, the center of mass of the disk will remain the same regardless of any external forces acting on the disk.

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