Four identical spheres of masses 2.0 kg each and radius 0.25 m are situated at the four corners of a square. One side of the square measures 3.00 m. Find the moment of inertia about an axis (a) passing through the center of the square and perpendicular to its plane, (b) passing through one of the masses and perpendicular to its plane, (c) passing through two adjacent masses parallel to the plane, and (d) in the plane running diagonally through two meters
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Four identical spheres of masses 2.0 kg each and radius 0.25 m are situated at the four corners of a square.
One side of the square measures 3.00 m. Find the moment of inertia about an axis (a) passing through the
center of the square and perpendicular to its plane, (b) passing through one of the masses and perpendicular
to its plane, (c) passing through two adjacent masses parallel to the plane, and (d) in the plane running
diagonally through two meters.
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- Problem One. A hollow cylinder with length L = 1.0 m, inner radius a = 1.0 m, and outer radius b = 2.0 m, has a mass density given by P=Lo , where p, =1.0k.. Find the moment of inertia of the cylinder (in kg-m³) if it spins around an axis along its center. 1.) (A) 99 (D) 76 (В) 46 (E) 53 (C) 31 A force given by F, = At , where A=4.0 % , is applied to the outer radius in a tangential direction. A second force given by F, = Bt², where B=3.0: , is also applied to the inner radius in a tangential direction that is opposite to the first force. If the cylinder starts from rest, find the power (in watts) delivered to the cylinder at 1 = 2.0 s. 2.) (A) 0.27 (B) 0.97 (C) 0.51 (D) 0.34 (E) 0.62 Find the angular displacement that is required for the cylinder to reach it's maximum angular speed. 3.) (A) 0.27 (B) 0.34 (C) 0.52 (D) 0.13 (E) 0.62Two spheres each with a radius of 5.0 cm and mass of 0.50 kg are free to slide along a thin rod with a of length 50 cm and a mass of 2 kg rotating counterclockwise about the center of the rod. Initially, the moment of inertia of the system is 0.255 kg*m². The beads slide to the end of the rod, which changes the moment of inertia to 0.377 kg*m. The tangential speed of either of the spheres after the beads have slid to the end is 20 m/s. What was the initial angular velocity? intial finalAn old grindstone, used for sharpening tools, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 300 N applied to its edge causes the wheel to have an angular acceleration of 0.848 rad/s2. (a) What is the moment of inertia of the wheel (in kg · m2)? kg · m2 (b) What is the mass (in kg) of the wheel? kg (c) The wheel starts from rest and the tangential force remains constant over a time period of 5.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period? rad/s
- A 65.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 480 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. (a) In what direction does the turntable rotate? counterclockwiseclockwise With what angular speed does the turntable rotate? rad/s(b) How much work does the woman do to set herself and the turntable into motion? JA 70.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 420 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. (a) In what direction does the turntable rotate? clockwisecounterclockwise With what angular speed does the turntable rotate? rad/s(b) How much work does the woman do to set herself and the turntable into motion? JAsap
- A 65.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 480 kg · m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. (a) In what direction does the turntable rotate? counterclockwise clockwise With what angular speed does the turntable rotate? ________rad/s(b) How much work does the woman do to set herself and the turntable into motion? __________JFrom 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 politPlease help me
- Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rb=2R are connected by a thin, uniform rod of length L=2R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a numerical factor in fraction form.Conceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 110 kg-m2. When one person is standing at a distance of 1.71 m from the center, the carousel has an angular velocity of 0.644 rad/s. However, as this person moves inward to a point located 0.641 m from the center, the angular velocity increases to 0.832 rad/s. What is the person's mass? | | Number i UnitsA 55.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 560 kg · m? and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. The woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth. (a) In what direction does the turntable rotate? O clockwise O counterclockwise with what angular speed does the turntable rotate? rad/s (b) How much work does the woman do to set herself and the turntable into motion?