Find the center of mass and the moment of inertia for the specified region between the parabola y = x^ 2/b and the line y = b
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A: Given, Masses are:m1=2.8 kgm2=3.7 kgm3=2.8 kgm4=3.7 kg The distance between the adjacent molecules…
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A: Given:mass of the disk, m = 133 kgradius of the disk, r = 1.79 mmass of the person, mp = 61.7…
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Q: A 103 kg horizontal platform is a uniform disk of radius 1.71 m and can rotate about the vertical…
A: mass of the uniform disc=103Kg Radius of the disc=1.71 m Moment of inertia of the disc,I=12MR2 (…
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Q: Relative to the origin of an x-y coordinate system, a particle is located at ?⃗ = 4.00 m ?̂+ 7.00 m…
A: r→ = 4i^ + 7j^ mp→ = 5i^ - 2j^ kgm/s
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Q: Using the definition of moment of inertia, calculate Icm, the moment of inertia about the center of…
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A: Given: m=2.0kgradius,r=0.25m To find: Moment of inertiaa)passing through centre of the…
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A: Let us consider a solid sphere of uniform density rotating about the z-axis. The sphere’s moment of…
Q: A 101 kg horizontal platform is a uniform disk of radius 1.61 m and can rotate about the vertical…
A: Given Mass of horizontal platform = 101 kg (uniform disk ) Radius of platform = 1.61 m Mass of a…
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A: Moment of inertia (MI) is the rotational analogue of mass in linear motion. It can be defined with…
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A: Moment of inertia of this system is given as I=Idisk +Idog+Iperson We know that Idisk=0.5M1R12…
Q: in a playground and runs with an initial speed of 4.2 m/s along a path tangent to the rim of a…
A: Given Mass of child, m=35 kgInitial speed of child, v=4.2 m/sRadius of merry-go-round, r=1.8 mMoment…
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A: The masses of the three uniform rods are given as, M1 = M2 = M3 = M The length of the three uniform…
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Q: Three metal balls of equal masses m= 1.25 kg are connected by massless rods as shown in the figure.…
A: Given, m1=m2=m3=1.25 kgx1=0,x2=4,x3=-3y1=3,y2=0,y3=-2
Q: A force acting through the point (x, y, z) where x 3, y = -6 and z = 6 is given by the vector: F =…
A: The moment is defined as the product of the distance traveled by an object and the force that acts…


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- Four masses are connected by 44.0cm long, massless, rigid rods. a) If their masses are mA = 156.0g, mB = 536.0g, mC = 524.0g, and mD = 497.0g, what are the coordinates of the center of mass if the origin is located at mass A? (Enter your x coordinate first followed by the y coordinate.) b) What is the moment of inertia about a diagonal axis that passes through masses B and D. The required picture is attached as wellA small, spherical asteroid of mass 6500000 kg and radius 7.6 m is stationary. The unsuspecting space rock is tangentially impacted by a Tesla roadster (mass 1320 kg) going 119000 km/h. In the following questions, assume the asteroid is uniform density and the coordinate system is set at the center of the asteroid, with the z direction aligned with its rotation axis post-impact. a) What is the magnitude of the car's linear momentum? IP carl | carl = b) What is the magnitude of the angular momentum of the car relative to the rotation axis of the asteroid just before impact? wf = kg m/s = kg m²/s c) After impact, assume the car sticks to the side of the asteroid, and treat it as a point mass. If angular momentum is conserved, what is the final angular velocity of the asteroid? rad/sAssume that (1) F = 10i +60j - 20k, acting at a point (8, 6, 4), and (2) two end points of a line L are A (2, 0, 4) and B (-7, 6, 2), respectively. Determine the moment of the force F about the line L. In the figure (a) is a force F and line L. (b) is the position vector r from A to the point of application of F.
- Show that the moment of inertia of a rectangular plate of mass m and sides ma?b? a and b about the diagonal is 6(a²+b?)The moment of inertia I of a cheap door of mass M = 4.00 kg (about an axis going through the hinges at the door frame) is I= (1/3) M · R², where R= 0.960 m is the width of the door. The door is initially open and at rest. The door suddenly is struck by a huge and heavy dart of mass m = 0.300 kg traveling perpendicular to the plane of the door at a speed vi = 20.0 m/s. The dart perforates the wooden door getting permanently stuck at the point of impact, which happened to be right next to the free vertical edge of the door (close to the handle). Because the dimensions of the dart are so small (even though they are exaggerated in the picture for clarity) compared to its distance R to the rotational axis (the distance from the hinge to the free vertical edge next to which the dart strikes the door, which is the width of the door R) we can treat the dart as a point mass. I remind you that we learned in class that the moment of inertia of a point mass is I, = m-R², where R is the…A 117 kg horizontal platform is a uniform disk of radius 1.67 m and can rotate about the vertical axis through its center. A 62.7 kg person stands on the platform at a distance of 1.11 m from the center, and a 29.5 kg dog sits on the platform near the person 1.39 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis. moment of inertia: kg · m?
- From a solid sphere of mass M and radius R, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is MR² (b) 32 √2π (a) 4MR² 9√3π (c) MR² 16 √2 G4MR² (d) 3√3π politConsider a compact disc as a thick walled cylinder of mass 16.0 g, and with an outer diameter of 11.6 cm and inner diameter of 4.6 cm. Find the (a) moment of inertia of the compact disc about an axis passing through its center and (b) moment of inertia of the compact disc about an axis passing through its edge parallel to the previous axis.A circular cone with constant density 1, base radius 6, and height 8 is placed so the axis of symmetry is on the z-axis. A cylindrical hole of radius 1 is drilled through the axis of symmetry. Find the moment of inertia of the remaining shape. (The moment of inertia about the z-axis will be the same no matter where the shape is placed along the z- axis and whether the shape is pointing up or pointing down.)
- At time t-0, a 4.61 kg particle has position vector 7 (5.00 m )7-(6.00 m) relative to the origin. Its velocity is given by 3=(-1.35² m/s ) for t in seconds. About the origin with t-12.8 s, what are (a) the particle's angular momentum and (b) the torque acting on the particle, both in unit-vector notation? (a) Number (b) Number Units UnitsA perfectly elastic ball bounces against a surface with a velocity vo = 2.4 m/s at an angle 0o = 45 degrees to the vertical. As a result of the impact, the ball bounces upward at an angle 0₁ = 23.2 degrees but also gains a topspin w₁ = 152 rad/s due to the rough surface. The ball has mass m = 10 grams and radius R = 16 mm. The moment of inertia of a solid sphere is /G = (2 m R²) / 5. The coefficient of restitution for the impact e = 1, so that energy can be assumed to be conserved during impact. g W₁ = 0 Vo 0₁ W₁ Calculate the magnitude of the velocity v₁ of the ball after impact. Ov=2.85 m/s O V = 2.4 m/s O V = 1.84 m/s O V = 1.67 m/s V₁Four small spheres, each of which you can regard as a point of mass 0.400 kg, are arranged in a square 0.700 m on a side and connected by extremely light rods. Find the moment of inertia of the system about an axis (a) through the center of the square, perpendicular to its plane (an axis through point O in the figure); (b) bisecting two opposite sides of the square (an axis along the line AB in the figure); (c) that passes through the centers of the upper left and lower right spheres and through point O. (Note: Change the value in the figure)