Hello, I need help on these question 6, 7, 8. Work would be appreciated so I could take notes on them, thank you so much for your time!

6. [-/2 Points] DETAILS SERPSE10 11.1.P.007. 0/6 Submissions Used A particle is located at the position vector r = (9.001 + 11.00j) m and a force exerted on it is given by F = (7.001 + 6.00j) N. (a) What is the torque acting on the particle about the origin? T = N . m (b) Can there be another point about which the torque caused by this force on this particle will be in the opposite direction and half as large in magnitude? O Yes O No (c) Can there be more than one such point? O Yes O No (d) Can such a point lie on the y-axis? O Yes O No (e) Can more than one such point lie on the y-axis? O Yes O No (f) Determine the position vector of one such point. (Give a point on the y-axis.) m Need Help? Read It7. [-/3 Points] DETAILS SERPSE10 11.2.OP.006.MI. 0/6 Submissions Used MY NOTES ASK YOUR TEACHER (a) A light, rigid rod of length { = 1.00 m joins two particles, with masses m, = 4.00 kg and my = 3.00 kg, at its ends. The combination rotates in the xy-plane about a pivot through the center of the rod (see figure below). Determine the angular momentum of the system about the origin when the speed of each particle is 6.20 m/s. (Enter the magnitude to at least two decimal places in kg . m /s.) i magnitude kg . m2/s direction ---Select--- (b) What If? What would be the new angular momentum of the system (in kg . m/s) if each of the masses were instead a solid sphere 11.5 cm in diameter? (Round your answer to at least two decimal places.) kg . m /s8. [-/4 Points] DETAILS SERPSE10 11.2.OP.009. 0/6 Submissions Used MY A counterweight of mass m = 5.20 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 9.00 cm and mass M = 1.40 kg. The spokes have negligible mass. M (a) What is the net torque on the system about the axle of the pulley? magnitude N . m direction ---Select--- (b) When the counterweight has a speed v, the pulley has an angular speed w = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. kg . m)v (c) Using your result from (b) and 7 = dL/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) m/s2