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a=g[ sinθ – F/Ncosθ ].

I have done this as shown below.

N is the normal reaction and F is friction.

N = mgcosθ

F = µN = µmgcosθ

mgsinθ – F = ma

mgsinθ – µmgcosθ = ma

a = g[ sinθ – µcosθ ]

but µ = F/N

a=g[ sinθ – F/Ncosθ ]

2. Determine an expression for the value of F/N where the only unknowns are the angle θ, the radius r and radius of gyration k.

I have tried this question and can’t get the right answer and need some help please.

I know

T = Iα

I = mk2 also for a solid disk I = 0.5mr2

α = a/r

m=N/gcosθ

Can anyone help with this question please?