Find the centre of mass of a semi circular plate

an suggests using polar coordinates to set up integrals for the mass and first moment of a semi-circular plate with a linearly varying density.
  • #1
Neilquintal
1
0
1. Find the centre of mass of a semi circular plate of radius R, the density of which linearly varies with distance, 'd' at the centre to a value '2d' at the circumference.
2. Xcom = (∫xdm)/M
3. I tried attempting the solution but I am not really knowing how to get dm in terms of dx
 
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  • #2
Since you have a semi-circular plate, why not use polar coordinates to set up your integrals for the mass and the first moment?
 
  • #3
Neilquintal said:
1. Find the centre of mass of a semi circular plate of radius R, the density of which linearly varies with distance, 'd' at the centre to a value '2d' at the circumference.




2. Xcom = (∫xdm)/M



3. I tried attempting the solution but I am not really knowing how to get dm in terms of dx
What is your equation for density as a function of x? What is your equation for dm as a function of x?

Chet
 

FAQ: Find the centre of mass of a semi circular plate

1. What is the definition of center of mass?

The center of mass is the point at which the entire mass of an object can be considered to be concentrated. It is the point where the object would balance if it were placed on a pivot.

2. How is the center of mass of a semi-circular plate calculated?

The center of mass of a semi-circular plate can be calculated by finding the midpoint of the diameter of the circle and measuring the distance from this point to the edge of the semi-circle. This distance will be equal to the radius of the circle.

3. What factors affect the center of mass of a semi-circular plate?

The center of mass of a semi-circular plate is affected by the distribution of mass within the plate and the shape of the plate. It also depends on the density and thickness of the material used to make the plate.

4. Why is finding the center of mass important?

Finding the center of mass is important for determining the stability of an object and predicting its motion. It is also used in engineering and design to ensure that objects are balanced and do not topple over.

5. Can the center of mass of a semi-circular plate change?

Yes, the center of mass of a semi-circular plate can change if the distribution of mass within the plate is altered or if the shape of the plate is changed. It can also change when external forces are applied to the plate, causing it to move or rotate.

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