Answer Happy

please answer all questions correctly and neatly
1. A primed coordinate system rotates about the z-axis with angular velocity ū = i' cost + ſ' sint relative to a fixed coordinate system, where t is the time. The origin of the primed system has position vector ſo = i't - ſ' + k't? with respect to the fixed system. The position vector of a particle is given by 1 = j't + k' relative to the moving system. Calculate the true velocity of the particle and the acceleration of the moving system. 2. A particle moving in a central force field located at r = 0 describes the spiral r=e. Show that the force varies as the inverse third power of r. 3. Using r = a(1 - cose) in the equation 2 f(r) ml2 [dar 2 (dr rt 202 ) -- rlde show that the force varies as the inverse fourth power of r. 4. Show that the position of a particle as a function of time t can be determined from the equation t = S[G(r)]-1/2 dr, where 2E 2 G(r) = + S romdr - 12 r2 m m