Question

A partiele in constrained to move along the inner surface
of a fixed hemispherical bowl. The number of degree of
freedom of the particle is​

Answer 1

Answer:

Degree of freedom is defined as the no. of independent co-ordinates that can be used tk define the motion of any particle. A free particle generally has 6 degrees of freedom ( one each for moving in x, y and z direction and 1 each for rotation about each axis). Here, as we are considering a point mass, we will only consider 3 degrees of freedom at max( movement along the 3 axes). Also, we have one constraint here regarding the motion of the particle, i.e. , moving inside a hemispherical bowl. So, in such cases, the total degrees of freedom are given by the no. of degrees of freedom without any constraints( 3 in this case) minus the no. of constraint equations ( 1 equation in this case).

So basically, degrees of freedom in this case = 3–1= 2.

However, if the body had some finite radius, the no. of degrees of freedom would have increased by 3(in this case).

533 viewsView 1 Upvoter · Answer requested by Namrata harbola

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