In the figure, two particles, each with mass m = 0.82 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.3 cm and mass M = 1.3 kg. The combination rotates around the rotation axis with angular speed w = 0.33 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy? M d Rotation axis (a) Number i .0332 Units kg-m^2 (b) Number i 0.00546 Units
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- The figure shows three 0.0186 kg particles that have been glued to a rod of length L=5.67 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 (a) Number Units (b) Number UnitsIn the figure, two particles, each with mass m = 0.84 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.6 cm and mass M = 1.0 kg. The combination rotates around the rotation axis with angular speed w = 0.28 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy? (a) Number 8 M Rotation axis (b) Number i M m Units UnitsA wheel with a radius of 0.23 m and a mass of 7.31 kg spins about its axis at 6.53 radians per second. What is the kinetic energy of the wheel in J? Treat the wheel as a cylinder of constant density.
- A hollow sphere (I=\frac{2}{3}mr^2I=32mr2) of radius R rotates about a diameter with an angular speed \omegaω. The sphere then collapses (magically) under the action of internal forces to a final radius of R/2 with no change in its mass. What is the final angular speed of the sphere?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 ball of mass M = 1.30 kg and radius r = 4.50 cm is attached to one end of a thin, cylindrical rod of length L = 14.0 cm and mass m = 0.880 kg. The ball and rod, initially at rest in a vertical position and free to rotate around the axis shown in the figure below, are nudged into motion. L m M (a) What is the rotational kinetic energy of the system when the ball and rod reach a horizontal position? J (b) What is the angular speed of the ball and rod when they reach a horizontal position? rad/s V(c) Vfreefall (c) What is the linear speed of the center of mass of the ball when the ball and rod reach a horizontal position? m/s (d) What is the ratio of the speed found in part (c) to the speed of a ball that falls freely through the same distance?
- In the figure here, three particles of mass m = 0.017 kg are fastened to three rods of length d = 0.15 m and negligible mass. The rigid assembly rotates about point O at angular speed w = 0.55 rad/s. About O, what are (a) the rotational inertia of the assembly, (b) the magnitude of the angular momentum of the middle particle, and (c) the magnitude of the angular momentum of the assembly? M (a) /= i (b) L₂ = i (c) Ltot 0 mIn the figure, two particles, each with mass m = 0.88 kg, are fastened to each other, and to a rotation axis at 0, by two thin rods, each with length d = 5.6 cm and mass M = 1.3 kg. The combination rotates around the rotation axis with angular speed w = 0.28 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy? M. M. Rotation axis (a) Number i Units (b) Number i UnitsThe 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 >