A hoop of mass M = 3.50 kilograms (kg) and radius R = 12.5 centimeters (cm) is resting on a flat surface. There is a constant, horizontal force with a magnitude F = 2.75 Newtons (N) acting at the center of mass of the hoop. As a result, the hoop begins to roll without slipping. The moment of inertia of a hoop is given by I = MR². Find the resulting linear acceleration of the hoop, in units of meters per second squared (m/s²). см X-
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- A hoop of mass M = 3.50 kilograms (kg) and radius R = 12.5 centimeters (cm) is resting on a flat surface. There is a constant, horizontal force with a magnitude F = 2.75 Newtons (N) acting at the center of mass of the hoop. As a result, the hoop begins to roll without slipping. The moment of inertia of a hoop is given by I = MR2. Find the resulting linear acceleration of the hoop, in units of meters per second squared (m/s2).A uniform thin rod of mass ?=3.47 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass ?=0.277 kg, are attached to the ends of the rod. What must the length ? of the rod be so that the moment of inertia of the three-body system with respect to the described axis is ?=0.987 kg·m2 ?An 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 200 N applied to its edge causes the wheel to have an angular acceleration of 0.804 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 4.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period? rad/s=
- A 8.44 kg particle with velocity 8.68 m/s 1.17 m/s is at x = 7.12 m, y = 9.61 m. It is pulled by a 8.42 N force in the negative x direction. About the origin, what are (a) the particle's angular momentum, (b) the torque acting on the particle, and (c) the rate at which the angular momentum is changing? (a) Number Units (b) Number Units (c) Number Units 111In the figure, two blocks, of mass m1 = 257 g and m2 = 337 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 492 g and radius R = 10.1 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T1 in the cord at the left and (c) the tension T2 in the cord at the right. M R T2 (a) Number i 0.095238 Units m/s^2 (b) Number Units (c) Number i UnitsA small block of mass m2 hangs from a massless rope wrapped around a pulley with radius of R. The moment of inertia of the entire pulley is I = 6m2(R)². Another block m1=2m2 is connected to the outer cylinder of the pulley via a horizontal massless rope. The coefficient of kinetic friction between the block and the horizontal surface is µg = 1 (i.e. the frictional force is f = m1g). When m2 is released from rest, what is the angular acceleration a of the block and pulley system? T, m, T. m, Pick the correct answer 最 1 g 18 1 g 10
- 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 rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.50 kg is attached to one end and a second mass m2 = 2.60 kg is attached to the other end of the rod. Treat the two masses as point particles.(a)What is the moment of inertia of the system in kg · m2? (b)If the rod rotates with an angular speed of 2.70 rad/s, how much kinetic energy, in joules, does the system have? (c)Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined, in kg · m2? (d)If the rod is of negligible mass, what is the kinetic energy, in joules, when the angular speed is 2.70 rad/s?A uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 5.99 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. |kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? |kg · m2/s