Centroid & Moment of Inertia Find the balance point and spin the fun!From shapes to structures, test how well you know the centers that hold mechanics together — because every body has its moment! 1 / 20 If a section has an axis of symmetry, the centroid lies — Away from the axis On the axis of symmetry At a corner At center of gravity of another body Due to symmetry, the centroid always lies along the axis that divides the shape evenly. 2 / 20 The product of inertia of a symmetrical section about centroidal axes is — Zero Minimum Maximum Constant In symmetrical figures, cross-products cancel out, making product of inertia zero. 3 / 20 The centroid of a quarter circle lies at a distance of — 4r/(3π) from both axes r/2 from both axes r/3 from both axes r/4 from both axes A quarter circle’s centroid lies symmetrically at equal distances 4r/(3π) from the axes. 4 / 20 The centroid of a semicircular wire lies at a distance of — r from the base r/2 from the base 4r/3π from the base 2r/π from the base For a wire (line), the centroid is at 2r/π from the base along the axis of symmetry. 5 / 20 The moment of inertia of a circular plate about a tangent in its plane is — (1/4) m r² m r² (3/4) m r² (1/2) m r² Using the parallel axis theorem, I = I₉ + m r² = (1/2 + 1/4) m r² = (3/4) m r². 6 / 20 The radius of gyration is defined as — I/m m/I √(I/m) I × m It represents the distance from the axis where the entire mass can be assumed concentrated to give the same I. 7 / 20 The unit of radius of gyration is — Meter Meter² Kilogram Newton Since k = √(I/m), the unit of radius of gyration is the same as length — meters. 8 / 20 The perpendicular axis theorem applies only to — Solid bodies Spheres Plane (2D) figures Cylinders It is valid only for flat laminae where Iₖ = Iₓ + Iᵧ. 9 / 20 The parallel axis theorem states — I = I₉ − m h² I = m h² I = I₉ + m h² I = I₉ × h² The moment of inertia about any parallel axis equals that about centroidal axis plus m h². 10 / 20 The moment of inertia of a hollow cylinder about its central axis is — m r² (1/2) m r² (2/5) m r² (3/5) m r² Since all mass is at the outer radius, I = m r² for a thin hollow cylinder. 11 / 20 The moment of inertia of a solid cylinder about its central axis is — (2/5) m r² (1/3) m r² (1/2) m r² m r² For a solid cylinder, I = ½ m r² about its central longitudinal axis. 12 / 20 The moment of inertia of a thin rod about one end is (1/12) mL² (1/2) mL² (1/4) mL² (1/3) mL² Shifting the axis from center to end using the parallel axis theorem gives I = (1/3) mL². 13 / 20 The moment of inertia of a thin rod about its center is — (1/12) mL² (1/2) mL² (1/4) mL² (1/3) mL² Using standard formulas, I = (1/12) mL² for a uniform rod rotating about its center. 14 / 20 Moment of inertia is expressed in — N·m N/m² kg·m² kg·m/s² It combines mass and the square of distance from the axis, hence its unit is kg·m². 15 / 20 The term moment of inertia refers to a body’s — Resistance to angular acceleration Mass distribution Elastic strength Linear momentum It measures how mass is distributed relative to an axis, resisting rotational motion. 16 / 20 The centroid of a right-angled triangle from the right angle is at — At the vertex One-third of both base and height Half of base and height Two-thirds of base and height In a right triangle, the centroid divides the medians in a 2:1 ratio, giving one-third distances from sides. 17 / 20 The centroid of a circle is at its — Center Circumference Chord Diameter Because a circle is perfectly symmetrical, its geometric center is also the centroid. 18 / 20 The centroid of a rectangle lies — Outside the shape At the intersection of its diagonals At its corner At mid-height The diagonals of a rectangle intersect at its center, which is also its centroid. 19 / 20 The centroid of a semicircular area lies at a distance of — r from the base r/3 from the base r/2 from the base 4r/3π from the base For a semicircle, the centroid is located along the axis of symmetry at 4r/3π from the flat edge. 20 / 20 The centroid of a triangle lies at the intersection of its — Medians Altitudes Bisectors Sides The centroid is the point where all three medians of a triangle meet, dividing each in a 2:1 ratio. Your score isThe average score is 0% 0% Restart quiz
