Answered: y m m M b a M м —х a a M m m Figure…

y m m M b a M м —х a a M m m Figure 10.19 (Example 10.10) Four spheres form an unusual baton. (a) The baton is rotated about the y axis. (b) The baton is rotated about the zaxis.

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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?
A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a uniform solid cylinder rotating around its axis, with moment of inertia I = 1/2 mr2. Consider a scenario in which the flywheel described in part (a) (r1 = 0.55 m, mass m1 = 16 kg, v = 45 m/s at the rim) is spinning freely at its maximum speed, when a second flywheel of radius r2 = 2.8 m and mass m2 = 11 kg is coaxially dropped from rest onto it and sticks to it, so that they then rotate together as a single body. Calculate the energy, in joules, that is now stored in the wheel. Return now to the flywheel of part (a), with mass m1, radius r1, and speed v at its rim. Imagine the flywheel delivers one third of its stored kinetic energy to car, initially at rest, leaving it with a speed vcar. Enter an expression for the mass of the car, in terms of the quantities defined here.
A wheel of radius 0.343 m, which is moving initially at 31.3 m/s, rolls to a stop in 296 m. Calculate the magnitudes of (a) its linear acceleration and (b) its angular acceleration. (c) The wheel's rotational inertia is 0.337 kg•m? 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
You are riding your bicycle down the street at a speed of 16 m/s. Your bicycle's frame has a mass of 6.0 kg, and each of its two wheels has mass 2.2 kg and radius 0.34 m. Each wheel can be thought of as a hollow hoop (assuming that the rim has much larger mass than the spokes). What is the total kinetic energy of the bicycle (in Joules), taking into account both the translational and rotational motion?
The figure shows three 0.0146 kg particles that have been glued to a rod of length L-5.58 cm and negligible mass. The assembly can rotate around a perpendicular axis through point O at the left end. If we remove one particle (that is, 33% of the mass), by what percentage does the rotational inertia of the assembly around the rotation axis decrease when that removed particle is (a) the innermost one and (b) the outermost one? (a) Number (b) Number Axis Units Units 0 m m m |a+d+d+
A block of mass mmm = 1.7 kg is attached to a string that is wrapped around the circumference of a wheel of radius RRR = 8.7 cm . The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially the wheel rotates with an angular speed ωω, causing the block to rise with a linear speed v = 0.33 m/s. Find the moment of inertia of the wheel if the block rises to a height of h = 7.6 cm before momentarily coming to rest.
A car is designed to get its energy from a rotating flywheel in the shape of a uniform, solid disk of radius 0.800 m and mass 600 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 5.30 ✕ 103 rev/min. (a) Find the kinetic energy stored in the flywheel (in J). (b) If the flywheel is to supply energy to the car as a 10.5 hp motor would, find the length of time in hours the car could run before the flywheel would have to be brought back up to speed.
The figure shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.4600 m and (total) mass M = 160.0 mg. The arrangement can rotate about a perpendicular axis through its central disk at point O. (a) What is the rotational inertia of the arrangement about that axis? Give your answer to four significant figures. (b) If we approximated the arrangement as being a uniform rod of mass M and length L, what percentage error would we make in using the formula in Table 10-2e to calculate the rotational inertia? ooooooooooo (a) Number i (b) Number i Units Units
A thin rod (length = 1.274 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge. The mass of the rod may be ignored, compared to the mass of an object fixed to the top of the rod. The rod, starting from rest, tips over and rotates downward. (a) What is the angular speed of the rod just before it strikes the floor? (Hint: Consider using the principle of conservation of mechanical energy.) rad/s (b) What is the magnitude of the angular acceleration of the rod just before it strikes the floor? rad/s2
Problem 7.09. In the Bald Eagle courtship ritual discussed Problem 7.03, the eagles will sometimes spin together. If the Eagles rotate with an angular velocity of 2.00 rev/s, a) treating their moment of inertia as that of a point mass 30.0 cm from their interlocked talons for each eagle, what is their combined rotational kinetic energy?
The figure shows three 0.0114 kg particles that have been glued to a rod of length L= 5.70 cm and negligible mass. The assembly can rotate around a perpendicular axis through point O at the left end. If we remove one particle (that is, 33% of the mass), by what percentage does the rotational inertia of the assembly around the rotation axis decrease when that removed particle is (a) the innermost one and (b) the outermost one? Axis m m (a) Number i Units (b) Number i Units >