Hi there, can you walk me through each part of the problem below? Can you help me understand the necessary steps to solve each part? Please also provide a response to each prompt so I can compare with my own solutions.

I have added a few formula reference that may be needed for the problem below. (Any unknown information can be found by searching on the internet/making reasonable or general assumptions)

Practice Problem: Helicopt erS. Understanding of torque is even more important for helicopter pilots. The large rotors provide lift by pushing air downward. Spinning the rotors fast enough requires a huge torque from the engine, and the reaction torque back on the body of the helicopter rotates the helicopter in the opposite direction. Every helicopter needs another rotor to counter this torque. This helicopter has a single main rotor that spins around a vertical axis and a small tail rotor that spins around a horizontal axis. The tail rotor provides a torque to balance the counter torque from the main rotor and to rotate (yaw) the aircraft when needed. (a) How long does it take to spin up the main rotor from rest? The engines provide a torque of about 1800 N-m. The main rotor has a radius (the length of one rotor blade) of 6.7m. Each of the four rotor blades has a mass of 42.8 kg. The maximum rotation rate of the main rotor is 290 rpm. (b) What is the rotational kinetic energy in the main rotor at full speed? (c) When the helicopter is moving forward, the rotor blades on one side are moving toward the front of the helicopter, while the blades on the other side are moving toward the back. If the maximum airspeed of the helicopter is 178 mph, what is the maximum tip speed of the rotor? The requirement for the tip speed to be less than the speed of sound limits the speed of helicopters. (d) The tail rotor needs to compensate for the counter torque from the main rotor. If the axis of the tail rotor is 25 ft from the axis of the main rotor, how much force does it need to apply to keep the helicopter balanced? (e) If the main rotor is rotating counterclockwise when viewed from above, what direction does the tail rotor's force have to be balance the helicopter? Work and Energy: Kinetic energy: K = =my Work: W = F . dr Work - Energy theorem: Wnet = AK Potential Energy (conservative Fc): W. = -AUc Conservation of Energy: Wnc = AK + AU Gravitational potential energy near the surface of the earth: U. = mgy Gmim2 Gravitational potential energy: UG = - r Spring potential energy: Usp = ka2 (for proper choice of coordinate system) Momentum and Impulse: Momentum: p = mu, Impulse: J = F dt ti Impulse-Momentum Theorem: J = Ap Conservation of Momentum: Ptot, f = Ptot, i (with no external forces)General: r(t) = x(t) ity(t) j+ z(t)k, dr du dar v (t ) = at ' a(t) = dt dt Newton's 2nd Law: For a an object of mass m: _ Fext = Fnet = ma Common Forces: Force due to gravity near surface of the earth: F , = mg Universal gravitation: |Fal = Gmim2 72 Spring force: Fsp = kell- lol in the direction to restore equilibrium Static friction: Kinetic friction: |FS | = HK N Kinematics with constant acceleration: u(t) = vo ta . (t -to) r(t) = ro+ vo . (t -to)+ za. (t-to)2 For a single dimension / axis x, we can also write: Uf x = Vox + 2ax(x5 -20) Simple Harmonic Oscillators: For a spring-mass system (k, and m): x(t) = Acos(wt + 4) 2 7T Where: W = T and T is the period of motion Circular Motion: de Arc Length: s = re Angular velocity: W = dt v = wr Centripetal acceleration: ac = = warReference for mements of inertia Axis Hoop about cylinder axis l = MR2 Axis Solid cylinder (or disk) about " cylinder axis , = ?- 2 Axis _ Thin rod about axis through i center J. to length it? \"'th Axis Solid sphere 2F? about any diameter _ zone I 5 Axis Hoop about t. any diameter Annular cylinder {or ring} about cylinder axis :=%tsi+s) Solid cylinder (or disk} about " oentral diameter Thin rod about axis through one i end i to length _ MP ' T Axis Thin . 2R spherical shell about any diameter l = ans? 3 Axis Slab about i axis through center b a If : M 12 Figure 10.21] Values of rotational inertia for common shapes of objects