Grade 12th passMechanics
a) Find the MI of section shown about an axis perpendicular to its plane and passing through point Ob) .
a) Find the MI of section shown about an axis perpendicular to its plane and passing through point O
b) .
1 Answer
Agrata Singh
Moment of inertia of any system depends upon its mass distribution aroun the reqd axis only
For part a of question consider a disc of mass M such that the axis passes throught its centre perpendicular to its plane. Now imagine compressing the disc in order to form the given arc.The mass of the arc is same as the disc and so is the mass distribution ( it can be visualised as more mass in the a given are however with the same distribution pattern as before)
With this theory, it can be easily said that the MI of given system will 1/2 MR2
Now for part b again MI abt axis passing through COM will be 1/2MR2. Using parallel axis theorem MI abt p will be 1/2MR2+MR2=3/2MR2
Other Related Questions on mechanics
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
mechanics
Last Activity: 9 Months ago
A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
11
21
31
41
A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
11
21
31
41
mechanics
Last Activity: 10 Months ago
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mmat the free end, where a small mass of 2 g is positioned. determine(i) The velocity of the end when passing through the zero position(ii) The acceleration at maximum displacement(iii) The maximum kinetic energy of the mass
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mm
at the free end, where a small mass of 2 g is positioned. determine
(i) The velocity of the end when passing through the zero position
(ii) The acceleration at maximum displacement
(iii) The maximum kinetic energy of the mass
mechanics
Last Activity: 3 Years ago
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
mechanics
Last Activity: 3 Years ago