How to Calculate the Center of Mass of a Semicircular Disk from an Arc?

AI Thread Summary
To calculate the center of mass (C.M.) of a semicircular disk from an arc, one can use the known C.M. of the semicircular arc and apply two methods. The first method involves treating the semicircular disk as a shell, subtracting a smaller disk's mass and taking the limit as the smaller radius approaches the larger one. The second method conceptualizes the disk as composed of many triangular layers, where the centroids of these triangles will collectively form an arc. Although the arcs differ in radius, their C.M. can be calculated by considering their mass distribution along the y-axis. Understanding these methods allows for accurate computation of the C.M. of both the semicircular arc and the disk.
jessicaw
Messages
54
Reaction score
0
i have calculated the C.M. of semi-circular arc of radius r and mass m.
How can i use this answer to calculate the C.M of semi-circular disk of radius r and mass m?
thanks:)

ps. how about the converse?
 
Physics news on Phys.org


just consider the disk is formed with many semi circular arcs

and for the converse case ,

there are 2 methods

1. consider the CM a semi circular shell, ie. a (disk) - (another disk with smaller radius), then take limit for the radius of the small one approach the bigger one

2. consider the semi circular disk as many triangular laminar...
 


sr-candy said:
just consider the disk is formed with many semi circular arcs

and for the converse case ,

there are 2 methods

1. consider the CM a semi circular shell, ie. a (disk) - (another disk with smaller radius), then take limit for the radius of the small one approach the bigger one

2. consider the semi circular disk as many triangular laminar...

"just consider the disk is formed with many semi circular arcs" but isn't the arcs different from each other? I thought of this at first but get stuck. How to do this techinically?
"2. consider the semi circular disk as many triangular laminar..."Triangle??confused.Why?and what do you mean by traingular "laminar"?
 


jessicaw said:
"just consider the disk is formed with many semi circular arcs" but isn't the arcs different from each other? I thought of this at first but get stuck. How to do this techinically?
"2. consider the semi circular disk as many triangular laminar..."Triangle??confused.Why?and what do you mean by traingular "laminar"?

1. yes the arcs are of different radius, but you have the CM of the arcs, so you can consider the mass of the arcs are all lying on the y axis, all you have to do is calculate the CM of these "CMs"

2. laminar means layer or plane etc. Just think that a semi circle is formed with many sectors, when the sectors become smaller, it will look like many triangle.
 


sr-candy said:
2. laminar means layer or plane etc. Just think that a semi circle is formed with many sectors, when the sectors become smaller, it will look like many triangle.

i understand this now, but how can i use this fact to calculate the C.M of arc? The C.M of triangle is the centroid but the centroid is not on the semicircular arc. So how to use this fact?
 


jessicaw said:
i understand this now, but how can i use this fact to calculate the C.M of arc? The C.M of triangle is the centroid but the centroid is not on the semicircular arc. So how to use this fact?

Why not? the centroids of these triangles will form an arc
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

The center of mass of a semicircular arc of non-negligible width
Replies
3
Views
2K
Find the center of mass of an arc
Replies
3
Views
2K
How to find centroid of a hemisphere using Pappus's centroid theorem?
Replies
27
Views
4K
Resultant field at the center of two semicircular current arcs
Replies
8
Views
2K
Why can't I treat the disk as a point mass?
Replies
3
Views
1K
Misunderstanding Work-energy theorem and center of mass properties
Replies
7
Views
2K
Calculate the speed and angle of the center of mass before a collision
Replies
3
Views
857
Body describes a closed trajecty on a free-to-spin disk
Replies
2
Views
1K
Center of mass and momentum- A question about systems
Replies
25
Views
1K
Finding z component of center of mass of a complex shape
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top