Consider a wheel of radius R = 1.50m rolling with constant velocity, without slipping, v = 18.1(i) m/s (where i is the unit vector), at the top of a horizontal cliff with height h = 20.0m. Take t = 0 as the time the wheel reaches the end of the cliff, i.e. the centre of the wheel has the position r(t) = (h+R)j. After this, the wheel falls freely. The point that is at the top of the wheel at t = 0 is denoted by P, i.e. r[p](t) = (h+2R)j
a) find the position of the centre of the wheel for t>t
b) at what time t[f] does the wheel hit the ground? Which point of the wheel hits the ground first? (I am assuming the wheel continues to rotate at constant w = v/R during the fall - w = omega)
c)find the position and velocity of point P of the wheel for t<t<t[f]. make a sketch of the position of P as a function of time
d) find the acceleration a[p] of point P for t<t<t[f]. for t = 0.125s, resolve the acceleration a[p] into parallel and perpendicular components, a[p](t) = a[par](t1) + a[per](t1). Make a sketch of the path of point P at time t~t, including v[p](t1) (the velocity of P), a[p](t1), a[par](t1) and a[per](t1)
NOT FOR THE FAINT HEARTED!