A thin wire of length (L) and uniform linear mass density (p) is bent into a circular loop. The moment of inertia of the circular loop about a tangent in its plane is : (a) (c) pL³ 8π² 3 pL³ 16T² (b) (d) 3 .5 pL³ 16 T² 3pL³ 8T²
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- In the figure, two particles, each with mass m = 0.78 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.5 cm and mass M = 1.3 kg. The combination rotates around the rotation axis with angular speed ω = 0.32 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy?The figure shows three 0.0186 kg particles that have been glued to a rod of length L=5.67 cm and negligible mass. The assembly can rotate around a perpendicular axis through point O at the left end. If we remove one particle (that is, 33% of the mass), by what percentage does the rotational inertia of the assembly around the rotation axis decrease when that removed particle is (a) the innermost one and (b) the outermost one? Axis (a) Number Units (b) Number UnitsThe wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh=0.262 m and mass 4.32 kg, and two thin crossed rods of mass 9.09 kg each. Imagine replacing the wagon wheels with uniform disks that are td=6.51 cm thick, made out of a material with a density of 7370 kg/m3. 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 pulley with moment of inertia I = 0.75 kg-m² and radius R = 15 cm is mounted on a wall. A light string is wrapped around the pulley with a mass m = 2.0 kg attached to the end. The pulley rotates as the mass falls. Use Newton's second law to calculate the acceleration of the mass. Check that your formula gives the expected behavior when I →0. => To help get started, the free body diagrams m and the pulley is shown below. T m Write down Newton's second law for each diagram. Use (and explain) the relationship R a = RO TIL R TA war-wolf, or trebuchet, is a device used during the Middle Ages to throw rocks at castles and now sometimes used to fling pumpkins and pianos. A simple trebuchet is shown in the figure below. Model it as a stiff rod of negligible mass 3.00 m long and joining particles of mass m₁ = 0.120 kg and m₂ = 55.0 kg at its ends. It can turn on a frictionless horizontal axle perpendicular to the rod and 15.5 cm from the particle of larger mass. The rod is released from rest in a horizontal orientation. Find the maximum speed that the object of smaller mass attains when it leaves the trebuchet horizontally. m/s m₂ Need Help? Read It 3.00 m m₂ eThe wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.368 m and mass 5.46 kg, and two thin crossed rods of mass 8.23 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0588 m thick, 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? 0.267 %3D Enter numeric value
- The figure shows three 0.0146 kg particles that have been glued to a rod of length L-5.58 cm and negligible mass. The assembly can rotate around a perpendicular axis through point O at the left end. If we remove one particle (that is, 33% of the mass), by what percentage does the rotational inertia of the assembly around the rotation axis decrease when that removed particle is (a) the innermost one and (b) the outermost one? (a) Number (b) Number Axis Units Units 0 m m m |a+d+d+The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.474 m and mass 4.70 kg, and two thin crossed rods of mass 8.23 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0651 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? rd = mwhat is the angular momentum of the of the Sun? It has a mass of 1.99 x 1030 kg. It has a radius of 696.3 x 106 m. It rotates with a linear velocity of 2200 m/s.
- The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ʼn = 0.315 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 ta = 0.0588 m thick, made out of a material with a density of 7370 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? ℗ la ro rd = mThe wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.580 m and mass 5.65 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0525 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? ra =The figure shows three 0.0114 kg particles that have been glued to a rod of length L= 5.70 cm and negligible mass. The assembly can rotate around a perpendicular axis through point O at the left end. If we remove one particle (that is, 33% of the mass), by what percentage does the rotational inertia of the assembly around the rotation axis decrease when that removed particle is (a) the innermost one and (b) the outermost one? Axis m m (a) Number i Units (b) Number i Units >