Two solid spherical masses mı = 2.51 kg and m3 = 1.48 kg with radii r1 = 0.21 and r2 = 0.14, are attached to the end of a massive rigid rod of mass m2 = 1.00 kg, as shown in the below figure. The rod is attached to a massive cylinder of mass m4 = 3.2 kg and radius r4 = 0.14 m, and is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through point P a distance l1 = 0.83 m and l = 0.52 m. The bar is released from rest in the horizontal position at t = 0.
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- The figure shows a uniform disk that can rotate around its center like a merry-go-round. The disk has a radius of 1.8 cm and a mass of 22 grams and is initially at rest. Starting at time t = 0, two forces are to be applied tangentially to the rim as indicated, so that at time t = 1.3s the disk has an angular velocity of 210 rad/s counterclockwise. Force F₁ has a magnitude of 0.105 N. What is magnitude F₂? F Number Units F2A Texas cockroach of mass 0.246 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has a radius 18.0 cm, rotational inertia 3.36 x 10³ kg-m?, and frictionless bearings. The cockroach's speed (relative to the ground) is 2.75 m/s, and the lazy Susan turns clockwise with angular velocity wo = 3.31 rad/s. The cockroach finds a bread crumb on the rim and, of course, stops. (a) What is the angular speed of the lazy Susan after the cockroach stops? (b) Is mechanical energy conserved as it stops? (a) Number Units (b)A uniform, solid sphere of radius 5.75 cm and mass 3.75 kg starts with a purely translational speed of 3.75 m/s at the top of an inclined plane. The surface of the incline is 1.75 m long, and is tilted at an angle of 34.0' with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed vz at the bottom of the ramp. U2 = m/s terms of use contact us help about us privacy policy careers 2 tv P MacBook Air ) F12 F11 F10 II F8 F9 F7
- A solid cylinder is mounted above the ground with its axis of rotation oriented horizontally. A rope is wound around the cylinder and its free end is attached to a block of mass 55.0 kg that rests on a platform. The cylinder has a mass of 255 kg and a radius of 0.490 m. Assume that the cylinder can rotate about its axis without any friction and the rope is of negligible mass. The platform is suddenly removed from under the block. The block falls down toward the ground and as it does so, it causes the rope to unwind and the cylinder to rotate. (a) What is the angular acceleration, in rad/s², of the cylinder? rad/s2 (b) How many revolutions does the cylinder make in 5 s? rev (c) How much of the rope, in meters, unwinds in this time interval?The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.209 m and mass 5.08 kg, and two thin crossed rods of mass 8.66 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0462 m thick, made out of a material with a density of 7830 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?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.
- The figure shows a uniform disk that can rotate around its center like a merry-go-round. The disk has a radius of 2.5 cm and a mass of 24 grams and is initially at rest. Starting at time t = 0, two forces are to be applied tangentially to the rim as indicated, so that at time t = 1.2 s the disk has an angular velocity of 260 rad/s counterclockwise. Force F1 has a magnitude of 0.0988 N. What is magnitude F2? Number .164 Units NA thin, hollow sphere of mass 2.30 kg and radius 0.610 m is rolling on a horizontal surface with a constant angular speed of 61.0 rpm. What fraction of the kinetic energy is translational kinetic energy, and what fraction of the kinetic energy is rotational kinetic energy?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?
- A playground merry-go-round with an axis at the center (radius R = 1.5 m and rotational inertia | = 1.33 x 103 kgm²) is initially rotating at angular velocity wo = 1.1 rad/s (counter-clockwise). A girl of mass m = 39 kg is running at speed vo = 3.3 m/s in a direction tangent to the disk of the merry-go-round, intending to jump on to the point labeled with the green "x" (she is indicated by the purple circle in the figure). What is the angular momentum of the girl relative to the rotation axis of the merry-go-round? Your answer should be in kgm²/s, but enter only the numerical part in the box. R WoA bicycle tire has a mass of 2.52 kg and a radius of 0.348 m. (a) Treating the tire as a hoop, what is its moment of inertia about an axis passing through the hub at its center? kg · m2 (b) What torque is required to produce an angular acceleration of 0.738 rad/s2? N · m (c) What friction force applied tangentially to the edge of the tire will create a torque of that magnitude? NA wheel of radius 0.297 m, which is moving initially at 44.7 m/s, rolls to a stop in 262 m. Calculate the magnitudes of (a) its linear acceleration and (b) its angular acceleration. (c) The wheel's rotational inertia is 2.93 kg · m² about its central axis. Calculate the magnitude of the torque about the central axis due to friction on the wheel. (a) Number i Units (b) Number i Units (c) Number i Units