Moment applied on a circular disc

In summary, for both cases, a circular disc is hinged in the centre and a moment is applied. In the first case, the moment is applied at the centre resulting in the disc rotating with an angular acceleration. In the second case, the moment is applied at a point other than the centre, but the disc will still rotate about the centre. This is because the moment is a free vector and can act anywhere, causing rotation around the fixed point of the disc. This would not occur if there were no fixed axis, in which case the disc would rotate around its center of mass.
  • #1
chandran
139
1
moment on a circular disc(moment applied in the centre)
A circular disc is hinged in the centre. I am applying a moment at the centre. The result is that the disc will rotate with an angular acceleration "a"

moment on a circular disc(moment applied not in the centre)
A circular disc is hinged in the centre. I am applying a moment at some point in the disc but not at the centre. How can i calculate the angular frequency. What is the theory? Will the disc rotate?
 
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  • #2
For your moment not applied at the center, it will still rotate about the center. The moment is a free vector, it can act anywhere you put it. It will cuase rotation around the fixed point of the body, if that point allows for rotation in the direction of the moment.

EDIT: What I said applies for a couple moment, if that's what you mean.
 
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  • #3
i am not getting. pls elaborate.
 
  • #4
Because one is incorporating a fixed rotation axis for the disk, it does not matter where on the disk other than its axix that you apply a tangental force to initiate rotation about that axis.
This would NOT occur if there were no fixed axis. In that case, the disk would rotate around its center of mass, which can be substantially different that the location of a fixed axis.
With a "fixed axis", centered or not, you are "forcing" rotation to occur around that axis.
 

1. What is a moment applied on a circular disc?

A moment applied on a circular disc is a force that causes the disc to rotate about its center. It is a measure of the tendency of the force to cause rotational motion, and is typically measured in units of Newton-meters (N·m).

2. How is the moment applied on a circular disc calculated?

The moment applied on a circular disc is calculated by multiplying the force applied by the distance from the center of rotation to the point where the force is applied. This distance is known as the moment arm or lever arm, and is typically denoted by the letter "r". The formula for calculating moment is M = F x r.

3. What factors affect the moment applied on a circular disc?

The moment applied on a circular disc can be affected by the magnitude of the force applied, the distance from the center of rotation, and the direction of the force relative to the center of rotation. Additionally, the mass and distribution of mass on the disc can also affect the moment.

4. What is the relationship between moment and torque?

Moment and torque are often used interchangeably, but technically torque is a specific type of moment that is applied around an axis of rotation. Torque is calculated by multiplying the force applied by the perpendicular distance from the axis of rotation to the point where the force is applied.

5. How is the moment applied on a circular disc used in real-world applications?

The moment applied on a circular disc is an important concept in engineering and physics, and is used in a variety of real-world applications. It is an important factor in designing and analyzing mechanical systems such as gears, pulleys, and levers. It is also used in understanding the behavior of structures under different loads and forces.

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