A thin rod of length 1.6 meters has a non-uniform mass density given by p = c (x +a), where x measures from one end of the rod to the other. Find the rotational inertia of the rod, in kgm?, when rotated about the point x = 0, using the values a = .3 m and c = 3.6 kg/m².
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- Calculate the rotational inertia of a meter stick, with mass 0.67 kg, about an axis perpendicular to the stick and located at the 39 cm mark. (Treat the stick as a thin rod.) X kg · m2Suppose you exert a force of 172 N tangential to a 0.295 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.) (a) What torque (in N · m) is exerted? (Enter the magnitude.) N. m (b) What is the angular acceleration (in rad/s2) assuming negligible opposing friction? (Enter the magnitude.) |rad/s? (c) What is the angular acceleration (in rad/s?) if there is an opposing frictional force of 22.6 N exerted 1.75 cm from the axis? (Enter the magnitude.) |rad/s?Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia 3.17 kg·m2 about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 489 rev/min. The second disk, with rotational inertia 7.08 kg·m2 about its central axis, is set spinning counterclockwise at 858 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 858 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together?
- A 4kg ball with a 0.45-meter radius is initially at rest begins to roll and accelerate at a uniform rate to a velocity of 10 rad/s in 5 seconds. The rotational inertia of the ball is 0.243 kg*m^2. Calculate the magnitude of the torque on the ball. Answer must use the correct SI units.A cord is wrapped around the rim of a wheel 0.300 m in radius, and a steady pull of 38.5 NN is exerted on the cord. The wheel is mounted on frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel about this shaft is 5.35 kg⋅m2 Compute the angular acceleration of the wheel.A grindstone in the shape of a solid disk (mass M = 50.0 kg) and radius R = 0.200 m (moment of Inertia | = 1/2 MR^2) is rotating at 90.0 rad/s. You press a metal box against the rim with a force F = 180 N and the grindstone comes to rest in 10.0 s. There is a friction force between the grindstone and the box. Find the magnitude of the friction.
- A uniform disk of radius 0.507 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with the same mass as the disk is attached around the disk's rim. A tangential force of 0.243 N applied at the rim causes an angular acceleration of 0.117 rad/s^2. Find the mass of the disk.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)Two thin rods of length L are rotating with the same angular speed w (in rad/s) about axes that pass perpendicularly through one end. Rod A is massless but has a particle of mass 0.70 kg attached to its free end. Rod B has a'mass of 0.70 kg, which is distributed uniformly along its length. The length of each rod is 0.72 m, and the angular speed is 4.9 rad/s. Find the kinetic energies of rod A with its attached particle and of rod B. (a) KEA = i (b) KEB =