What is perpendicular axis theorem for moment of inertia?
The perpendicular axis theorem states that the moment of inertia of a planar lamina (i.e. 2-D body) about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two axes at right angles to each other, in its own plane intersecting each other at the point …
What is the moment of inertia of a rod about its axis?
The moment of inertia of a rod about an axis through its centre and perpendicular to it is 121ML2 (where M is the mass and L, the length of the rod).
What is the formula for perpendicular axis theorem?
Suppose we want to calculate the moment of inertia of a uniform ring about its diameter. Let its centre be MR²/2, where M is the mass and R is the radius. So, by the theorem of perpendicular axes, IZ = Ix + Iy.
What is its moment of inertia about an axis perpendicular to the stick through its center of mass?
τ=r⋅F=mr2α. Note that it matters where we choose the rotation axis. For example, the moment of inertia of a rod of length L and mass m around an axis through its center perpendicular to the rod is 112mL2, whereas the moment of inertia around an axis perpendicular to the rod but located at one of its ends is 13mL2.
What is perpendicular axis theorem prove it?
The theorem states that the moment of inertia of a plane laminar body about an axis perpendicular to its plane is equal to the sum of moments of inertia about two perpendicular axes lying in the plane of the body such that all the three axes are mutually perpendicular and have a common point.
What is perpendicular axis theorem 11th?
Perpendicular Axis Theorem: The moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body.
On what factors does moment of inertia depends and find moment on inertia of a rod?
Moment of inertia depends on both mass and its distribution relative to the axis of rotation.
What is the moment of inertia of a rod about one end?
The moment of inertia about the end of the rod can be calculated directly or obtained from the center of mass expression by use of the Parallel axis theorem. I = kg m². If the thickness is not negligible, then the expression for I of a cylinder about its end can be used.
Why do we use perpendicular axis theorem?
Application of Perpendicular Axis Theorem This theorem is most useful when considering a body which is symmetrical about two out of the three axes. If the value of the moment of Inertia about these two axes is known, then we can easily calculate the Moment of Inertia about the third axis by applying this theorem.
Does the moment of inertia depend on the axis of rotation?
The moment of inertia of an object usually depends on the direction of the axis, and always depends on the perpendicular distance from the axis to the object’s centre of mass.