I need someone(s) to check my answers to these problems. Force F = (7.0 N) i + (-10.0 N) j acts on a particle with position vector r = (-3.0 m) i + (1.0 m) j (a) What is the torque on the particle about the origin? (b) What is the angle between the directions of r and F? (If there is no torque, enter 0.) What I did (a) τ = r × F = 23k (b) r = √( 32 + 12) = √10 F = √(72 + 102) = √149 r ∙ F = √1490 23 = √(1490)sinθ θ = 36.573° I got part a right, but part b is wrong. Is it because of the way I did it, math error, or rounding??? Or did I mess up the sign? Next one... At the instant of Figure 11-40, two particles move in an xy plane. (Let the +z axis extend out of the page.) Particle P1 has mass 7.3 kg and speed v1 = 2.2 m/s, and it is at distance d1 = 1.3 m from point O. Particle P2 has mass 3.1 kg and speed v2 = 3.6 m/s, and it is at distance d2 = 2.8 m from point O. (a) What is the magnitude of the net angular momentum about point O? I subtracted the magnitudes to get 10.37, which is correct. (b) What is the direction of the net angular momentum about point O? +x -x +y -y +z -z I know that it has to be +z or -z, but I'm not sure which. I think particle 1's angular momentum goes into the page (-z) and particle 2 goes out of the page (+z). Since the magnitude of particle 2's angular momentum is greater, the net angular momentum would go in the +z direction. Is this correct? Next... In Figure 11-48, two skaters, each of mass 50 kg, approach each other along parallel paths separated by 3.0 m. They have opposite velocities of 1.9 m/s each. One skater carries one end of a long pole with negligible mass, and the second skater grabs the other end of it as she passes. The skaters then rotate around the center of the pole. Assume that the friction between skates and ice is negligible. It asked several questions involving calculations which I got right. Then it asked this. (d) What provided the energy for the increased kinetic energy? centrifugal force centripetal force internal energy of the skaters gravity friction (more than one could be correct) Since gravity doesn't do any work, friction is neglible, centripetal force doesn't do any work and centrifugal force doesn't exist I'm guessing it's only internal energy of the skaters? Last one... A man stands on a platform that is rotating (without friction) with an angular speed of 1.0 rev/s; his arms are outstretched and he holds a brick in each hand. The rotational inertia of the system consisting of the man, bricks, and platform about the central vertical axis of the platform is 7.5 kg·m2. By moving the bricks the man decreases the rotational inertia of the system to 2.0 kg·m2. It asked for some calculations which I got correct, but then comes this mc. (c) What provided the added kinetic energy? None of these is correct. the momentum of the platform None of these is correct. the man moving the weights further away from his body the man pulling the weights closer to his body I'm not sure why the teacher put none of these is correct in there twice, but that one's probably not correct. I think the correct answer is the man pulling the weights closer to his body. Anyone agree?