1. (10 points) A thin plate of mass m was cut in the shape of a parallelogram as shown. Determine the mass moment of inertia of the plate with respect to the y -axis. Please simplify your answer as much as possible. A A' B'

Q: Shown is the cross section of an idler roller. Determine its mass moment of inertia and its radius…

A: Write the expression of the mass of the bronze part. Write the expression of the mass of the…

Q: The moments of inertia of the area A about the parallel p- and p' -axes differ by 15 10 mm. Compute…

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Q: By the method of this article, determine the rectangular and polar radii of gyration of the shaded…

A: Write the given data. ro=ari=0.36a

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.

A: Given profile for finding the moment of inertia Given curve

Q: 100 mm Problem (3) A 3-mm thick piece of aluminum sheet metal is cut and bent into the machine…

A: mass od all the sections m1 = ρV1 = 2270×(0.24×0.18×0.003) = 0.294 kgm2 = ρV2 =…

Q: 11B) The area moment of inertia about centroidal axis is the area moment of inertia about a parallel…

A: option C is the correct answer  i.e. less than

Q: Aluminum wire with a weight per unit length of 0.033 lb/ft is used to form the circle and the…

A: Given data Weight per unit length of the aluminium wire = 0.033 lb/ft Radius of the ring r = 16 in…

Q: Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to…

A: In the given figure, the product of inertia because of the rectangular part will be zero since it is…

Q: The area shown is revolved about the x axis to form a homogeneous solid of revolution of mass m .…

A: Given Revolution mass = m To find in terms of m The mass moment of inertia about X axis Y axis

Q: a. Determine the moments of inertia of the shaded area shown in (Fig. 4-a) with respect to the x and…

A: In the strength of material, stress & strain is determined for various material. Stress is the…

Q: The welded assembly is made of a uniform rod which weighs 0.481 lb per foot of length and the…

A: Given:Mass of uniform rod=0.481 lb/ftMass of semicircular plate=8.3 lb/ft2Radius of semicircular…

Q: Construct a table and determine the moment of inertia of the following area with respect to…

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Q: Determine the moments of inertia about the tangent axis x-x for the full ring of mass m1 and the…

A: To find: Ixx = ? for full ring Ixx = ? for half ring

Q: Determine the moments of inertia I, and I, of the area shown with respect to centroidal axes…

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Q: A 8 lb metal sheet lies on xy-plane. Given that the length a=7 in and the centroid of the metal…

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Q: 1B. Derive from first principles the moment of inertia for a right-angled triangle about its base…

A: Consider a right-angle triangle with base b and height h as shown below,

Q: inertia of the assembly with respect to (a) the x axis, (b) the y axis, (c) the z axis. (The density…

A: Given data: The density of steel, ρ = 7850 kg/m3. Represent the diagram into three segments,…

Q: OD = 150 mm 1400 mm Determine (to two decimal places) the mass moment of inertia (in kg.m2) of the…

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Q: Using the parallel-axis theorem, determine the product of inertia of the area shown with respect to…

A: kyФот,J1 I20 mm20mm1TrommGommloklimm100mmlommBy applying parallel anis theorem, looduct of Inertia…

Q: Activity 2. A rectangle is 4cm by 6cm. determine its polar moment of inertia with respect to an axis…

A: Moment of inertia about an x-axis Ixx=13bh3=13(6)(4)3=128 cm4 Moment of inertia about a y-axis…

Q: Which of the following is the measure of distribution of the body's mass about the axis about which…

A: Answer :- Radius of gyration

Q: For the shaded area shown, given that a = 14 cm; b a a - t 2а A. Determine the moment of inertia…

A: Given Data a=14 cm b=12 cm t=1.5 cm Shaded area is symmetrical about y-axis then centroid lies on…

Q: 4.5 cm 4.5 cm 15 cm 20 cm 9 cm 20 cm

A: Part Area Ai yi Ai yi rectangle 1 29 ×24 = 696 12 8352 rectangle 2 -20 ×15= -300 -16.5 -4950…

Q: Consider a rigid body consisting of three rods, each of length L = 0.7 m, and mass m = 9 kg. C the…

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Q: The thin plate shown is composed of a rectangular plate of mass 102 kg and a quarter-circular plate…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: the ratio moment of inertia of a rectangular shape to triangular shape having the same base width(b)…

A: The moment of Inertia of a plane area with respect to x and y axis respectively is defined by the…

Q: An isosceles triangle has a 10 cm base and a 10 cm altitude. Determine the moment of inertia of the…

A: Given data: b=h=10 cm Need to determine the moment of inertia of the triangular area relative to a…

Q: 2. Find the moment of inertia of the following structure. A hoop of mass mr = 4mo and radius a about…

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Q: B/34 Determine the moment of inertia about the x-axis of the portion of the homogeneous sphere…

A: It is known that the moment of inertia of a solid sphere is Here, Ro is the radius of the sphere.…

Q: The assembly is made of the slender rods that have a mass per unit length of 2 kg/m .  Determine…

A: Find the mass moment of inertia about point O. Mass per unit length = 2 kg/m

Q: Determine the moments of inertia about the y-axis of the circular area without and with the central…

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Q: The moments of inertia of the area A about the parallel p- and p' -axes differ by 15*10ʻmm . Compute…

A: Given data Ip-Ip'= 15×106 mm4

Q: A solid cylinder with a radius of 3.9 cm has the same mass as a solid sphere of radius R Part A If…

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Q: Determine the transferred moment of inertia of Triangle on its Upper vertex when its dimension area…

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Q: Moment of inertia of square plate about the axis shown is axis M 130°

A: Mass moment of inertia of an area is defined as the product of mass of area and the distances of its…

Q: . The ratio of the moment of inertia of a at of a square plate for equal depth, is (a) less than one…

A: Answer : Width=DDepth=DDiameter=D

Q: 4. Rods are attached end to end, made of L same material and have same thickness. Determine the mass…

A: given; lets take mass of each rod =m

Q: For the shape showed below, determine the location of the horizontal centroidal axis and the…

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Q: Question 4 Calculate the moments of inertia I, and I, of the composite region consisting of the…

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Q: The machine element shown in the figure is made of steel (Density: 7850 kg / m ^ 3). Determine the…

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Q: For the composite arca shown below: (a) Locate the centroid i (from the left edge) and ỹ (from the…

A: The given composite area can be divided into six parts Part 1:- A rectangle ABCD whose sides are 40…

Q: determine the centroidal polar moment of inertia of a rectangle 100mm wide by 200 mm high

A: Given:- h=200mm b=100mm To find:- Polar moment of inertia about centroidal axis

Q: ree uniform slender rods of mass M and attached to each other to form a mutually or in the figure on…

A: Three uniform skricker poles of mass and length Leach are rigidly appended to one another to shape a…

Q: Determine (to two decimal places) the mass moment of inertia (in kg.m2) of the system shown above…

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Q: 2сm h 2cm b 2сm

A: Center of gravity Center of gravity is a point in a body where all the mass of body is concentrated.…

Q: (e) Use integration and the parallel axis theorem to find the mass moment of inertia of the…

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Q: Part A Determine the moment of inertia of the composite area about the a axis. Express your answer…

A: Given Data: The value of a is 5.4 in.

Q: 3- Determine the moment of inertia of shaded area shown in Fig. below with respect to x-axis. 10cm…

A: Mass moment of inertia measures a body resistance towards rotational motion. If a body have more…

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.