. The moment of inertia of a thin uniform rod of length (1) and mass (M) about an axis passing through mid point between centre point and one end and perpendicular to its length is : (a) (c) MI² 3 M1² 12 (b) (d) MI² 9. ADbrb of . 7 48 MP²
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- The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.421 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0651 mthick, made out of a material with a density of 8290 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?Chapter 10, Problem 067 GO The figure shows a rigid assembly of a thin hoop (of mass m = 0.28 kg and radius R = 0.13 m) and a thin radial rod (of length L = 2R and also of mass m = 0.28 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? Hoop Rod Rotation axis Number Units the tolerance is +/-2% Click if you would like to Show Work for this question: Open Show WorkThe wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.421 m and mass 5.46 kg, and two thin crossed rods of mass 7.37 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0588 mthick, made out of a material with a density of 5990 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?
- Force F = (- 7.7 N )i + (4.6 N )j acts on a particle with position vector 7 = (2.5 m )i + (4.2 m )j. What are (a) the %3D magnitude of the torque on the particle about the origin and (b) the angle between the directions of 7 and F ? (a) Number i Units (b) Number i UnitsFrom 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 politThe wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.156 m and mass 5.08 kg , and two thin crossed rods of mass 7.37 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0651 m thick, made out of a material with a density of 5530 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?
- A solid cylinder with a radius of 4.0 cm has the same mass as a solid sphere of radius R. If the cylinder and sphere have the same moment of inertia about their centers, what is the sphere’s radius?The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.209 m and mass 5.08 kg, and two thin crossed rods of mass 8.66 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0462 m thick, made out of a material with a density of 7830 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?Question 5 only.......
- Problem 3: Suppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass. Part (a) First calculate the moment of inertia (in kg m2) when the skater has their arms pulled inward by assuming they are cylinder of radius 0.11 m. sin() cos() tan() 7 8 9 HOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 3 cosh() tanh() cotanh() END ODegrees O Radians Vol BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Part (b) Now calculate the moment of inertia of the skater (in kg m?) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.825 m long rods extending straight out from the center of their body being rotated at the ends.The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.156 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks = 0.0525 m thick, made out of a material with a density of 5990 kg per cubic meter. If the new wheel is to have the same ta %3D moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? = PA rdThe angular momentum vector of a precessing gyroscope sweeps out a cone as shown in the figure below. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by t/L, where ris the magnitude of the torque on the gyroscope and L is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earth's axis of rotation precesses about the perpendicular to its orbital plane with a period of 2.58 x 10 yr. Model the Earth as a uniform sphere and calculate the torque on the Earth that is causing this precession. N m