they are placed at two points in space defined by radius vector say r1 and r2′
then a centre of mass-a point can be defined about which the mass moments are equal. say that point to be R.
then R= (m1.r1 +m2.r2)/M
where M=m1+m2 i.e total mass of two body system.
so the mass moment of total mass = mass moments of the individual masses.
If no net external forces are acting on above two bodies then the masses can move under the action of internal forces, they may collide and change their speeds or there may be momentum changes .
but the centre of mass which represents the total mass of the system at any instant can move only with uniform velocity as no external forces are acting on the ‘system’ as a whole.
the momenta of the bodies before collision and after collision will be same as internal forces can not change the total momentum of the system;
M.R = m1.r1 +m2.r2
If the masses are moving with time M.(dR/dt ) = m1.( dr1/dt ) + m2.(dr2/dt)
so centre of mass will be moving with a velocity which can change if
F(ext) acts and leads to M.(dP/dt) if F(ext) =0 P the momentum will be constant.
however if m1 pushes m2 and in turn gets pushed by m2…these are pair of internal forces and it will add up to zero because of their directions and magnitude. however these internal forces will change the velocities of the two bodies.
so , one can conclude that-
If the net external force on a system of particles is zero, then (even if the velocity of individual bodoes changes), there is a point associated with the distribution of bodies that moves with zero acceleration (constant velocity).
This point is called the “center of mass” of the system.
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Answer:
suppose you have two bodies of masses m1 and m2.
they are placed at two points in space defined by radius vector say r1 and r2′
then a centre of mass-a point can be defined about which the mass moments are equal. say that point to be R.
then R= (m1.r1 +m2.r2)/M
where M=m1+m2 i.e total mass of two body system.
so the mass moment of total mass = mass moments of the individual masses.
If no net external forces are acting on above two bodies then the masses can move under the action of internal forces, they may collide and change their speeds or there may be momentum changes .
but the centre of mass which represents the total mass of the system at any instant can move only with uniform velocity as no external forces are acting on the ‘system’ as a whole.
the momenta of the bodies before collision and after collision will be same as internal forces can not change the total momentum of the system;
M.R = m1.r1 +m2.r2
If the masses are moving with time M.(dR/dt ) = m1.( dr1/dt ) + m2.(dr2/dt)
so centre of mass will be moving with a velocity which can change if
F(ext) acts and leads to M.(dP/dt) if F(ext) =0 P the momentum will be constant.
however if m1 pushes m2 and in turn gets pushed by m2…these are pair of internal forces and it will add up to zero because of their directions and magnitude. however these internal forces will change the velocities of the two bodies.
so , one can conclude that-
If the net external force on a system of particles is zero, then (even if the velocity of individual bodoes changes), there is a point associated with the distribution of bodies that moves with zero acceleration (constant velocity).
This point is called the “center of mass” of the system.
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