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). CM X- F
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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 ?A small pine tree has a mass of 19 kg. Its center of mass is located at 0.87 m from the ground. Its trunk is sawed though at ground level, causing the tree to fall, with the severed trunk acting as the pivot point. At the instant the falling tree makes a 16° angle with the vertical, the angular acceleration of the tree is 2.6 rad/s. What is the moment of inertia of the tree?
- A baton twirler in a marching band complains that her baton is defective. The manufacturer specifies that the baton should have an overall length of L= 70.0 cm and a total mass between 960.0 and 970.0 g (there is one 365-g objects on each end). Also according to the manufacturer, the moment of inertia about the central axis passing through the baton should fall between 0.0900 and 0.0950 kg/m². The twirler (who has completed a class in physics) claims this is impossible. Submit "What is the minimum mo answer to three significant figures.) kg m² L Submit 2) What is the maximum moment of inertia? (Express your answer to three significant figures.) kg. m² 3) Who's right? of inertia? (Express your The twirler is correct. The manufacturer is correct. Submit + +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 Units
- A 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 10A 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 17.0-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.490 kg-m², and its radius is 0.150 m. When turning, friction at the axle exerts a torque of magnitude 3.20 N-m on the reel. If the hose is pulled so that the tension in it remains a constant 26.0 N, how long does it take to completely unwind the hose from the reel? Neglect the mass and the thickness of the hose, and assume that the hose unwinds without slipping.