Finding Mass Center of a Circular Disc with Hole & Weight

AI Thread Summary
The discussion centers on determining the center of mass of a circular disc with a hole and an additional weight attached. The center of mass is influenced by the position of the hole and the mass added at point P, which affects its location relative to the geometric center of the disc. The angle of suspension and the mass distribution play crucial roles in finding the equilibrium position. It is noted that for small values of k, the hole's impact may shift the center of mass to the left, contrary to the initial assumption. The calculation of k is essential for understanding the overall balance of the system.
Roadtrip
Messages
3
Reaction score
0
Why do we take the Center of mass to be on the right side rather than on the left?
A uniform circular disc of radius 4a with a circular hole of radius 2a made in the disc.
The mass of L is m and a particle of mass km is now fixed to L at the point P. The system is now suspended from the point S and hangs freely in equilibrium. The diameter ST makes an angle a with the downward vertical through S, where tana=5/6
Find the value of K

Disc before adding weight km at point P has a mass m of coordinates (10/3,0).
https://s26.postimg.org/qczk9oc3t/image.jpg[URL]https://s26.postimg.org/lsdduqseh/image.jpg
 
Last edited:
Physics news on Phys.org
Roadtrip said:
I am having difficulty uploading a picture
You can use the "upload" button here, or upload it at some image hoster and add a link here.

I don't see images in the linked thread.
 
image.jpg
image.jpg
 
The center of mass is on a line that goes from S downwards. If P is lower than Q, then it is to the right of the geometric center of the large disk. It does not have to be - for small values of k the hole is more important and the center of mass would be to the left.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Finding the Center of Mass of a Uniform Disc: A Non-Calculus Approach
Replies
3
Views
4K
Finding the center of mass of a solid hemisphere
Replies
19
Views
3K
Finding Center of Mass of Disc with Hole
Replies
12
Views
2K
Moment of Inertia of a Spinning Record with a Hole in Center
Replies
13
Views
4K
How to find centroid of a hemisphere using Pappus's centroid theorem?
Replies
27
Views
4K
How Does External Force Affect a Rotating Disc and Ring System?
Replies
6
Views
3K
Is Mass Variation Relevant in Analyzing Tape Dynamics Down a Ramp?
Replies
7
Views
2K
Rotation of Rigid Bodies: Rotating stick with disc on top
Replies
9
Views
2K
Two-Disk Pendulum Oscillation: Find Period w/ Mass M & Radius R
Replies
7
Views
2K
Proving generality of moment of inertia
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top