Moment of inertia of a body about a given axis is 1.5 kg m². Initially, the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of 20 rad/s² must be applied about the axis for a duration of
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- A piece of wood is pressed against a spindle sanding disk which is a uniform disk with a radius of 0.090 m, rotating at an initial angular velocity of 37.0 rad/s (ωi = 37.0 rad/s). This motion results in a constant tangential frictional force of magnitude f = 9.00 N and causes the sanding disk to come to a complete stop in = 25.0 s. (a) Small pieces of wood get removed from the large piece of wood with a speed equal in magnitude to the tangential velocity of the rim of the sanding disk (and in a direction tangent to the disk). What is thespeed of the pieces of wood when the disk is rotating at its initial angular velocity of ωi.(b) What is the angular acceleration α of the sanding disk.(c) How many revolutions does the disk complete before coming to a stop?In the figure, a wheel of radius 0.234 m is mounted on a frictionless horizontal axis. The rotational inertia of the wheel about the axis is 0.586 kg-m2. A massless cord wrapped around the wheel's circumference is attached to a 4.00 kg box. The system is released from rest.When the box has a kinetic energy of 4.00 J, what are (a) the wheel's rotational kinetic energy and (b) the distance the box has fallen? Assume free-fall acceleration to be equal to 9.81 m/s2. M (a) Number Units (b) Number UnitsA solid sphere with a radius of 0.41 and a mass 0.3 is set to rotate about its center. After a time of 14.6 s, its rotational kinetic is 28.7 J. What is its constant angular acceleration
- A solid disk is initially at rest and has a moment of inertia of 0.0830 kg·m2. If a net torque of 0.0770 N⋅⋅⋅⋅m is applied to the disk, what rotational kinetic energy will it have after 19.3 s have elapsed?A uniform disk (1=1/2 mR2) has a mass of 3 kg and a radius of 2m. The disk is mounted on frictionless bearings and is used as a turntable. The turntable is initially rotating at 120 rpm (revolutions per minute, convert it to rad/s). A hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable. (HINT: Note that some of the information given is not needed! Think which conservation law(s) apply.) The final angular momentum of the system is closest to: L = Submit [5] ΑΣΦ Request Answer ? kg. m²/s 4A wheel consists of a rim (ring) with a mass of 1.3kg and a radius of 0.45m and four equally-spaced spokes (rods) that run from the center of the wheel to the edge of the rim. Each spoke has a mass of 0.15kg and a length equal to the radius of the wheel. What is the total rotational inertia of the wheel about its center?
- A disk with a rotational inertia of 7.46 kg·m2 rotates like a merry-go-round while undergoing a torque given by τ = (5.54 + 7.56t) N · m. At time t = 1.00 s, its angular momentum is 8.05 kg·m2/s. What is its angular momentum at t = 3.00 s?Two wheels A and B in the figure are connected by a belt that does not slip. The radius of B is 4.30 times the radius of A. What would be the ratio of the rotational inertias IA/IB if the two wheels had (a) the same angular momentum and (b) the same rotational kinetic energy? (the absolute tolerance for the answer of a is ± 0.001)(the absolute tolerance for the answer of b is ± 0.0001)A 150 g baseball is pitched at 32.8 m/s and spinning at 42 rad/s. You can treat the baseball as a uniform solid sphere of radius 3.7 cm. What fraction (in %) of its kinetic energy is rotational?