Home
Class 11
PHYSICS
State and prove theorem of perpendicular...

State and prove theorem of perpendicular axes.

Text Solution

Verified by Experts

The moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of its moment of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body.

The figure shows a planar body. (Whose thickness is very small compared to their other dimensions like length, breadth or radius). An axis perpendicular to the body through a point O is taken as the Z-axis. Two mutually perpendicular axes lying in the plane of the body and concurrent with Z-axis, means passing through O are taken as the X and Y-axis.
The theorem states that `I_(z)=I_(x)+I_(y)` where are the moment of inertia about X-axis and Y-axis respectively.
If planar body is in YZ-plane then
`I_(x)=I_(y)+I_(z)`
If planar body is in XZ-plane, then
`I_(y)=I_(x)+I_(z)`
This theorem be applicable to planar body only.
Promotional Banner

Topper's Solved these Questions

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    KUMAR PRAKASHAN|Exercise SECTION-A HOTS|3 Videos

  • SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

    KUMAR PRAKASHAN|Exercise SECTION-A (TRY YOURSELF (VSQs))|94 Videos

  • QUESTIONS ASKED IN JEE - 2020

    KUMAR PRAKASHAN|Exercise Question|16 Videos

  • THERMAL PROPERTIES OF MATTER

    KUMAR PRAKASHAN|Exercise Question Paper (Section - D) (Answer following in brief :) Each carry 4 marks|1 Videos

Similar Questions

Explore conceptually related problems

State and prove theorem of parallel axis.

(a) Prove the theorem of perpendicular axes. (Hint : Square of the distance of a point (x, y) in the x-y plane from an axis through the origin perpendicular to the plane is x^(2)+y^(2) ). (b) Prove the theorem of parallel axes. (Hint : If the centre of mass is chosen to be the origin Sigmam_(1)(r_(i)=0) .

Will the theorem of perpendicular axis be applicable to a solid sphere?

Write carnot theorem.

The coordinates of a point are the perpendicular distance from the ____ on the respectives axes.

If a line is drawn through the centre of a circle to bisect a chord, then prove that it is perpendicular to the chord.

if one of the lines given by the equation ax^2+2hxy+by^2=0 coincides with one of the lines given by a'x^2+2h'xy+b'y^2=0 and the other lines representted by them be perpendicular , then . (ha'b')/(b'-a')=(h'ab)/(b-a)=1/2sqrt(-a a' b b')

L and L' are end points of latus rectum of parabola y^2 = 4ax and M' and M are foot of perpendiculars from there points to line x = 0 then are of LL'M'M = .........

Theorem of perpendicular axis be applicable to which type of body?

Prove that the bisectors of two adjacent angles of a parallelogram are perpendicular to each other.