A ring-shaped space station can be approximated as a thin ring 60 meters in diameter with a mass of 500,000 kg. The space station has a set of thrusters able to exert equal and opposite forces as shown below. If we want to cause an angular acceleration of .1 rad/s² in the space station, what is the force required from each thruster? thruster a =.1 rad/s Finruster thre

A 5kg lacrosse stick has a moment of inertia about a transverse axis through its center of gravity of 8 kg.m2. When a player swings the stick at an opponent, the axis of rotation is through the end of stick, 80 cm from the center of gravity of the stick. What is the moment of inertia relative to this swing axis? A 4 kg lacrosse stick has a radius of gyration of 60cm about a transverse axis through its center of gravity. When a player swings the stick at an opponent, the axis of rotation is through the end of stick, 120cm from the center of gravity of the stick. What is the moment of inertia relative to this swing axis?

(b) An electric motor lifts a mass of 500 kg from the ground to a height of 30 m in 1.5 minutes. Calculate the motor's output power during operation. The gravitational acceleration, g, is 9.81 m. s-².

4) This Atwood's machine includes two blocks connected by a cable, going over a pulley without slipping. Block 1 (30.0 kg) is connected to a spring (70.0 N/m), and slides on a horizontal surface with a coefficient of kinetic friction of 0.0100. Block 2 is 50.0 kg, and hangs vertically from the cable. The pulley is a disk with a radius of 0.500 m, and its moment of inertia about the center of mass is 10. 0 kg-m“. a) Draw the three free body diagrams, and write out Newton's 2nd Law for each. b) Derive the equation of motion (inhomogeneous 2nd order ODE) for this system. c) Use u-substitution to rewrite this as a homogeneous 2nd order ODE. d) Assume the position x as a function of time t is of the form x(t) = A cos (wt + p) I disk for undamped natural frequency w, phase angle P, and amplitude A. The initial conditions are: x(0) v(0) = -3. 00 m/s. Solve for the position of the mass as a function of time (you need to solve for w, 4, and A). = 2. 00 m and Mz