Week 8 Homework Assignment

1. (P.288 Prob.2)Four point masses of 3.0kg each are arranged in a square on massless rods.(Gig.8.54). The length of a side of the square is 0.50m. What is the rotational inertia for rotation about an axis (a) passing through masses B and C? (b) passing through masses A and C? (c) passing the center of the square and perpendicular to the plane of the square?
   
2. (P.289 Prob.14) A child of mass 40.0kgis sitting on a horizontal seesaw at a distance of 2.0m from the supporting axis. What is the magnitude of the torque about the axis due to the weight of the child?
3. A flywheel of mass 182kg has an effective radius of 0.62m (assume the mass is concentrated along a circumference located at the effective radius of the flywheel). (a) What torque is required to bring this wheel from rest to a speed of 120rpm in a time interval of 30.0s? (b) How much work is done during the 30.0s?
4. (P.291 Prob.30)A mountain climber is rappelling down a vertical wall (Fig.8.64). The rope attaches to a buckle strapped to the climber's waist 15cm to right of his center of gravity. If the climber weighs 770N,  find (a) the tension in the rope and (b) the magnitude and direction of the contact force exerted by the wall on the climber's feet.
   
5. (P.292 Prob.36) A person is doing leg lift with 3.0-kg ankle weights. She is sitting in a chair with her legs bent at a right angle initially. The quadriceps muscles are attached to the patella via a tendon; the patella is connected to the tibia by the patellar tendon, which attaches to bone 10.0cm below the knee joint (Fig.8.69). Assume that the tendon pulls at an angle of 20.0° with respect to the lower leg, regardless of the position of the lower leg. The lower leg has a mass of 5.0kg and its center of gravity is 22cm below the knee. The ankle weight is 41cm from the knee. If the person lift one leg, find the force exerted by the patellar tendon to hold the leg at an angle of (a) 30.0° and (b) 90.0° with respect to the vertical.
6. (P.293 Prob.44) A grinding wheel, with a mass of 20.0kg and a radius of 22.4cm, is a uniform cylindrical disk. (a) Find the rotational inertia of the wheel about its central axis. (b) When the grinding wheel's motor is turned off, friction causes the wheel to slow from 1200rpm in 4.00s? Assume that the frictional torque is the same regardless of whether the motor is on or off.
7. (P.293 Prob.50)A solid sphere of mass 0.600kg rolls without slipping along a horizontal surface with a translational speed of 5.00m/s. It comes to an incline that makes an angle of 30° with the horizontal surface. Neglecting energy losses due to friction. (a) what is the total energy of the rolling sphere? and (b) to what vertical height above the horizontal surface does the sphere rise on the incline?
8. (P.294 Prob. 62) A skater is initially spinning at a rate of 10.0rad/s with a rotational inertia of 2.50kg·m² when her arm are extended. What is her angular velocity after she pulls her arm in and reduces her rotational inertia to 1.60kg·m²?