Using similar parallel cutting planes, the whole object is assumed to cut into several elementary strips. STEP 4 – DIVIDE WHOLE OBJECT INTO NUMEROUS STRIPS ( MI ) of elementary strip about YY' axis will be –ĭM = ( dA \ x ) x = x^2 \ dA = x^2 \ L \ dx + m_n ) = \left ( \sum \right ) can be neglected. Hence, mass of body ( M ) = ( m_1 + m_2 +.The body is consisting of numerous particles of small masses ( m_1, \ m_2 \.Consider about a body of mass ( M ) rotating about an axis.
Radius of gyration of a body is defined as the radius of an imaginary circular ring whose mass is equal to the mass of that body. See numerical problems based on this article. Here ( M ) is the mass of a body and ( x ) is the distance of centre of gravity of the body from the axis of rotation.Its magnitude is given by \left ( M x^2 \right ).Here ( A ) is the area of two dimensional object like a lamina and ( x ) is the distance of geometrical centroid of area from the axis of rotation.Its magnitude is given by \left ( A x^2 \right ).Here ( F ) is the magnitude of force and ( x ) is the distance of line of action of this force from the axis of rotation.Its magnitude is given by \left ( F x^2 \right ).īasically, moment of inertia is of three forms – In short form moment of inertia is written as ( MI ).Moment of inertia is also known as Second Moment or Moment of Moment. If the body is rotating or revolving about an axis.If the body is moving in circular motion or in curved path.Moment of inertia of a body comes into action and resist the changes in motion for following cases – curvilinear motion or rotary motion, is called Inertia of moment or Moment of inertia. What is the ratio of moment of inertia of a ring to a disc? Given that both have masses in the ratio 2:1 & radii in the ratio 1:2 respectively.Ĭlarification: Moment of inertia of ring = MR 2& moment of inertia of disc = MR 2/2.Property of a material by virtue of which a body resists to change in its state of motion along a circular path i.e. Moment of inertia of thin spherical shell ‘I 2’= 2/3 MR 2.Ħ. What will be the moment of inertia of a very thin spherical shell of the same mass and radius as that of the solid sphere?Ĭlarification: Moment of inertia of solid sphere ‘I 1’ = 2/5 MR 2 = 10kgm 2. The moment of inertia of a solid sphere is 10kgm 2. What is the moment of inertia of a rod about an axis passing through the centre and perpendicular to its central axis? Given that mass of rod is 1kg, length = 10cm.Ĭlarification: Let the moment of inertia be I.Īnd M & I be the mass and length of rod respectively.ĥ. Radius of gyration ‘k’ is given by the expression: I = Mk 2Ĥ. Find its radius of gyration.Ĭlarification: Moment of inertia of disc = MR 2/2 = 10*1/2 = 5kgm 2. A solid disc has a mass of 10kg and radius 1m. And hence, it has more moment of inertia.ģ. Thus, the summation of product of mass and perpendicular distance from the axis squared of each particle will be more for the hollow cylinder.
Which one will have the greater moment of inertia about the central axis?Ĭlarification: The hollow one will have greater density as both have the same mass and it has to be distributed uniformly. Two cylinders have the same mass and radius. As the body having a particular value of moment of inertia can achieve any value of angular velocity depending on the torque applied on it.Ģ.
But, it doesn’t depend on the angular velocity. It depends on perpendicular distance hence, it will depend on orientation and distance of particles from the axis. Moment of inertia, of a spinning body about an axis, doesn’t depend on which of the following factors?Ĭlarification: Moment of inertia is the summation of product of mass and perpendicular distance from the axis squared of each particle. Physics Multiple Choice Questions on “Moment of Inertia”.ġ.
0 kommentar(er)
