State the parallel axis theorem and perpendicular axis theorem.

State the parallel axis theorem and perpendicular axis theorem.
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Answer :

Parallel axis theorem: It states that the M. I. of a plane section about any axis parallel to the centroidal axis is equal to the M. I. of the section about the centroidal axis plus the product of the area of the section and the square of the distance between the two axes. 

Perpendicular axis theorem: It states MI of a plane lamina about an axis perpendicular to the plane of lamina and passing through the centroid of the lamina is equal to the addition of the moments of inertia of the lamina about its centroidal axes.
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Related questions

State and explain perpendicular axis theorem of moment of Inertia.

Description : State and explain perpendicular axis theorem of moment of Inertia.

Last Answer : Perpendicular axis theorem: It states MI of a plane lamina about an axis perpendicular to the plane of lamina and passing through the centroid of the lamina is equal to the addition of the moments of ... OY are mutually perpendicular and OZ is the axis perpendicular to plane XY of the lamina.

Which of the following relations is used to represent theorem of perpendicular axes? (H = Vertical axis, I = Moment of inertia and K = Radius of gyration) a. IPQ = Ixx + AH2 b. IPQ = Ixx + Ak2 c. Izz = Ixx + Iyy d. Izz + Ixx + Iyy = 0

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Last Answer : c. Izz = Ixx + Iyy

Secondary Linear Axes U,V & W are ……… to X,Y & Z-axis. a.Perpendicular b.Parallel c.Rotational d.All of the above

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Last Answer : b.Parallel

Polar moment of inertia is a.Applicable to masses whereas moment of inertia is applicable to area only b.The moment of inertia for an area ralative to a line or axis which is out the plane of area c.Same as moment of inertia d.The moment of inertia for an area relative to a line or axis parallel to the centroidal axis e.The moment of inertia for an area relative to a line or axis perpendicular to the plane of the area

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Last Answer : e. The moment of inertia for an area relative to a line or axis perpendicular to the plane of the area

Longitudinal vibrations are said to occur when the particles of a body moves A Perpendicular to its axis B Parallel to its axis C In a circle about its axis D None of the mentioned

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Last Answer : B Parallel to its axis

Longitudinal vibrations are said to occur when the particles of a body moves (A) Perpendicular to its axis B (B) Parallel to its axis (C) In a circle about its axis (D) None of the mentioned

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Last Answer : (B) Parallel to its axis

Longitudinal vibrations are said to occur when the particles of a body moves a) perpendicular to its axis b) parallel to its axis c) in a circle about its axis d) none of the mentioned

Description : Longitudinal vibrations are said to occur when the particles of a body moves a) perpendicular to its axis b) parallel to its axis c) in a circle about its axis d) none of the mentioned

Last Answer : b) parallel to its axis

Longitudinal vibrations are said to occur when the particles of a body moves a) perpendicular to its axis b) parallel to its axis c) in a circle about its axis d) none of the mentioned

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Last Answer : b) parallel to its axis

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If the perpendicular distance of a point P from the X-axis is 5 units and the foot of the perpendicular lies on the negative direction of X-axis, then the point P has -Maths 9th

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The perpendicular distance of the point P(3, 4) from the Y-axis is -Maths 9th

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Find the co-ordinates of that point on the curve`y^(2)=x^(2)(1-x)` at which the tangent drawn is perpendicular to X-axis.

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Assertion (A): In equilibrium position, the journal inside a journal bearing remains floating on the oil film. [IES-1995] Reason (R): In a journal bearing, the load on the bearing is perpendicular to the axis of the journal. (a) Both A and R are individually true and R is the correct explanation of A (b) Both A and R are individually true but R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true

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Description : Which of the following formulae is used to calculate tangential stress, when a member is subjected to stress in mutually perpendicular axis and accompanied by a shear stress? a. [(σ x - σ y )/2 ]sin θ - τ cos 2θ b. [(σ x - ... τ cos 2θ c. [(σ x - σ y )/2 ]sin θ - τ 2 cos θ d. None of the above

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Description : A theodolite is said to be in perfect adjustment if (A) Rotation axis is vertical to the transit axis (B) Transit axis is perpendicular to line of collimation (C) Line of collimation sweeps out a vertical plane while the telescope is elevated or depressed (D) All the above

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Description : In a theodolite (A) The telescope axis is perpendicular to transit axis (B) The axis of rotation is perpendicular to transit axis (C) The telescope axis, the transit axis and the rotation axis pass through the centre of theodolite (D) All the above

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A vertical column has two moments of inertia (i.e. Ixx and Iyy ). The column will tend to buckle in the direction of the (a) axis of load (b) perpendicular to the axis of load (c) maximum moment of inertia (d) minimum moment of inertia

Description : A vertical column has two moments of inertia (i.e. Ixx and Iyy ). The column will tend to buckle in the direction of the (a) axis of load (b) perpendicular to the axis of load (c) maximum moment of inertia (d) minimum moment of inertia

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Which of the following in theodolite work is imperfect adjustment of the instrument (a) Error due to line of collimation being perpendicular to the horizontal axis (b) Error due to axis not to perpendicular of the vertical axis (c) Error due to imperfect graduation (d) Error due to eccentricity of vernires (e) All of the above*

Description : Which of the following in theodolite work is imperfect adjustment of the instrument (a) Error due to line of collimation being perpendicular to the horizontal axis (b) Error due to axis not to perpendicular ... to imperfect graduation (d) Error due to eccentricity of vernires (e) All of the above*

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is this statement true or falsethe converse of the alternate exterior angle theorem guarantees that line L and line n are parallel.?

Description : is this statement true or falsethe converse of the alternate exterior angle theorem guarantees that line L and line n are parallel.?

Last Answer : 1

what postulate or theorem guarantees that line L and line N are parallel?

Description : what postulate or theorem guarantees that line L and line N are parallel?

Last Answer : converse of the corresponding angles postulate

What is the moment of inertia acting on a rectangle of width 15 mm and depth 40 mm about base by using theorem of parallel axes? a. 320 x 103 mm4 b. 300 x 103 mm4 c. 240 x 103 mm4 d. 80 x 103 mm

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The Snell law is applicable for perpendicular polarisation and the Brewster law is applicable for parallel polarisation. State True/False. a) True b) False

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Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other. -Maths 9th

Description : Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other. -Maths 9th

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Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other. -Maths 9th

Description : Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other. -Maths 9th

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In a trapezium ABCD, AB is parallel to CD, BD is perpendicular to AD. AC is perpendicular to BC. If AD = BC = 15 cm and AB = 25 cm, -Maths 9th

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Are the lines parallel, perpendicular, or neither3x + 4y = 103y – 4x = 4?

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is this statement true or falseTwo lines that are perpendicular to the same line are parallel.?

Description : is this statement true or falseTwo lines that are perpendicular to the same line are parallel.?

Last Answer : 1