centre of mass Flashcards
what is centre of mass
its basically the point which represents the average of the whole mass….it can be assumed that the whole mass of the body is concentrated at that point…rotation of the body is symmetric about that point… its situated near the heavier mass
what is centre of mass from a reference point
it is the distance from the reference point where the mass is concentrated
formula of centre of mass
x1m1+x2m2+x3m3……../m1+m2+m3…….
so basically the mass is getting cancelled
if there are two masses and the position of one of them is taken as the reference point then what is the ratio of the distance between m1 and com to distance between m2 and com
m2:m1
if masses are taken in a cartesian plane then where is centre of mass
m1r1+m2r2+m3r3…../m1+m2+m3….
where r1,r2,r3…. are the position vectors of the masses
r1 r2 r3… are basically the distances of the masses from the origin
how to find the x coordinate y coordinate and z coordinate of the centre of mass
m1x1+m2x2+m3x3……/m1+m2+m3…..
do the same thing for y and z coordinate
if the mass of a particle is uniformly distributed then what is the coordinated of the centre of mass
the normal formula of com is x1m1+x2m2+x3m3……../m1+m2+m3…….
here the mass is uniformly distributed so each small part of the particle has a mass of dm
so the x coordinate of com is integration of xdm/integration of dm( as the denominator represents the total mass of the whole object and the numerator is basically the summation of all the x coordinates of each segment of the particle)
DO THE SAME THING FOR Y AND Z COORDINATES
what is the trick while solving uniform distributed mass questions
you have to consider that a dm section of a mass has a length dx
whenever theres a question related to circumcircle of circle or semicircle or sphere then what is the trick to solve this
for this kinda shit u have to consider a small angle d(theta) and solve from there
what is the length of a small segment on circumference
Rd(theta)
whenever theres a question related to area of circle or semicircle or shit like that then what is the trick to solve this
then you have to take a thin section of the circle as the and assume it have an area dA. this section of area must be parallel to circumference
what is the centre of mass of a system of particles
x1M1+x2M2+x3M3……./M1+M2+M3…..
here M1 is the mass of system1 and x1 is the centre of mass of system1. M2 is the mass of system 2 and x2 is the centre of mass of system2 and so on…….
if the mass of the object is uniformly distributed then the centre of mass of the system is integration of xdm/integration of dm
here x is the centre of mass of each system of mass
what is meant by centre of mass of system of mass
it is the centre of mass of a collection of points
what is an example of system of mass
while finding the centre of mass of an uniformly distributed semicircle we have to take small sections of area parallel to the circumference. there will be infinite number of such areas so we consider each area as a system of mass and we use the above formula
what is the com of the circumference of a semicircle
2R/pi
what will be the com of a small section of a circle with angle d(theta)
the small section can be considered as a triangle
the answer is 2R/3
in any question related to 1d 2d and 3d how do we approach the problem
you have to take a small section one dimension less than the dimension given in the question
if it is 1d you have to convert it into something without dimensions (like a small section of length like dl)
if its 2d you have to convert it into 1d(like area of circle into circumference of circle)
if its 3d take a small section of volume(convert volume into area)
what is the shortcut while finding the com of 3d and 2d circular shapes
in a 3d circular shapes just divide it into concentric circles horizontally with a thickness of dy
in a 2d circular shapes just divide it into concentric circles parallel to circumference with a thickness of dx
what is the relation between radius of concentric circle and radius of sphere
if h is the height of the concentric circle and R is the radius of the big circle and r is the radius of the concentric circle then R^2=r^2+h^2
what is a common mistake made
the r of the concentric circle is different from R of main circle
in a cone how to relate dl dh r R h and h
by similarity and using the vertical angle
what is the com of the area of a semicircle
4R/3pi
what is the com of a uniformly distributed cone
H/4
what is the com of a hollow cone
2H/3