From a solid sphere of mass M and radius R, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is MR² (b) 32 √2n (a) 4MR² 9√√3π (c) MR² 16 √2T (4MR² 3√√3π (d)
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- Review Conceptual Example 2 before attempting this problem. The moon has a diameter of 3.48 x 106 m and is a distance of 3.85 x 108 m from the earth. The sun has a diameter of 1.39 x 10⁹ m and is 1.50 x 1011 m from the earth. Determine (in radians) the angles subtended by (a) the moon and (b) the sun, as measured by a person standing on the earth. (c) Determine the ratio of the apparent circular area of the moon to the apparent circular area of the sun. These calculations determine whether a total eclipse of the sun is really "total." (a) Number i (b) Number (c) Number i Units Units UnitsThe 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+Problem 2: A wheel with radius r= 1.8 m has a tangential force F = 14.2 N acting on it as shown. F Part (a) What is the magnitude of the torque about the center of the wheel, in N•m? N•m sin() cos() tan() 7 8 9 НОMЕ cotan() asin() acos() E ↑^^| 4 5 6. atan() acotan() sinh() 1 3 cosh() tanh() cotanh() END O Degrees Radians VO BACKSPАСЕ DEL CLEAR Part (b) What is the direction of the torque?
- Your answer is partially correct. Review Conceptual Example 2 before attempting this problem. The moon has a diameter of 3.48 x 106 m and is a distance of 3.85 x 108 m from the earth. The sun has a diameter of 1.39 x 10⁹ m and is 1.50 x 10¹1 m from the earth. Determine (in radians) the angles subtended by (a) the moon and (b) the sun, as measured by a person standing on the earth. (c) Determine the ratio of the apparent circular area of the moon to the apparent circular area of the sun. These calculations determine whether a total eclipse of the sun is really "total." (a) Number 0.00904 (b) Number i 0.0093 (c) Number i 0.945 Units rad Units Units rad No unitsA 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 6.05 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/sA 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
- A force vector, F = 3i− 12j, acts at a distance vector of r = 0.2i m from the axis of rotation on a wheel. It has a moment of inertia of 3 kgm^2. If we assume the full mangitude of the torque causes rotation, what is the angular acceleration caused by the force?In 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 Units