Question

i was wondering if anyone could give me a better method to solve this problem

given T=dL/dt, calculate the time taken for the top to precess one revolution about the origin. give answer in terms of R, d and w
note
L=Iwr (angular momentum) (w = angular velocity)
I=MR^2/2 (moment of inertia) (M=mass, R=radius of disc(mass))
T = -10dsin(z)(sina i + cosa k) (i, j and k are unit vectors)
r= dsin(z)cos(a) i + dcos(z) j - dsin(z)sin(a) k (vector along shaft to spinning mass)

the solution i got, but i feel like it is too complex
RHS = Iw dr/dt
=Iw dr/da * da/dt (chain rule) (da/dt = w)

Answer 1

ran out of letters
=IW * -sin(z)(sin(a) j + cos(a)k)
=1/2 *mR^2 W^2 * -sin(z)(sin(a) j + cos(a)k)
but t = -10md* sin(z)(sin(a) j + cos(a)k)
10md=1/2 *m R^2 W^2
w^2 = 20d /R^2 (but w = da/dt)
da/dt=20d/R^2w (da = 360 degrees / 2pi)
dt =w pi R^2 / 10d (dt = time final - time initial = 0)
t=pi w R^2 /10d