Rotational Mechanics - Question

[BBAI BBAI]

As there is no acceleration of centre of mass the CM moves in a straight line its falls downwards so the end point moves L/2 Distance.

 

[Doc Al]

As there is no acceleration of centre of mass the CM moves in a straight line its falls downwards so the end point moves L/2 Distance.

The center of mass is accelerated.

 

[ehild]

Edit:
Sorry. Normal reaction does not pass through CM, and so there will be net force on the CM downward. Will it be mg or mg-R ? I think former is correct. Also if a rod is pivoted at the end and it is left swing in a semicircle, will there be linear acceleration in its centre of mass ?

Sankalpmittal,

The rod is an extended body. You can imagine it as a system of point masses, connected to each other by internal forces.

To make it simpler, assume a system of two point masses m1 and m2, their position vectors r1 and r2. The external forces, F1 and F2 act on m1 and m2, respectively, and the internal force f12 is exerted by m2 on m1 and f21 = -f12 is exerted by m1 on m2.

You can write up Newton's II for each mass:

m1a1=F1+f12

m2a2=F2-f12

Add up the equations:

m1a1+m2a2=F1+F2 . (*) The internal forces cancel.

The position vector of the CM is defined as R_CM= (m1r1+m2r2)/(m1+m2). So (*) can be written in terms of the acceleration of the CM and the total mass M=m1+m2 of the system. : Ma_CM=F1+F2.

You can get the equivalent formula for a system of any number of point masses.

The CM of the extended body moves as if all the external forces acted on it. No matter at what point the external forces act: The CM will be accelerated by the sum of forces.


The rod in the problem is acted on by gravity and the normal force (reaction force R). Gravity acts at each mass element, but the resultant of the gravitational forces acts at the CM. The normal force acts from the ground, at the lower end of the rod. The CM is accelerated by the net force mg-R.

ehild

 

[sankalpmittal]

Sankalpmittal,

The rod is an extended body. You can imagine it as a system of point masses, connected to each other by internal forces.

To make it simpler, assume a system of two point masses m1 and m2, their position vectors r1 and r2. ...

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ehild

Thanks a lot everyone which includes ehild ! I get it now.

It was all the concept of the net force on centre of mass of the rod system.