Question

Wheel The wheel shown above has a mass of 30kg, a radius of 0.6m and a radius of gyration of kg = 0.25m. If the wheel is released from rest at the top of a ramp, determine the maximum angle of the ramp such that the wheel will roll down the ramp without slipping. The coefficient of static friction between the wheel and ramp is us = 0.2 and the coefficient of kinetic friction between the ramp and wheel is uk = 0.15.

Answer 1

Given Data : m= 30kg R = 0'6m KG=0.25m Ms = 0:2 , Hik=0'15. free body diagram of wheel :- F img cosa mg sino a my N. Equilibrium cuong Yo direction:- Efy = may N-mgcoso =0 N=mg coso - ci) equilibrium duong x-direction:- Efu = max. mase = mg sino - fs - cii) where, fo = MSN. (at the verge of impeding motion 2 from equation (2), max= mg since = USN. - Cin

Torque at centre of mass, :. T = Icm. x By taking moment about point 'o'. Т= Ғs XY I cm X = Fs XY = USNY. a. I ma = Msr mg coso. - 9x = 7d Cui) and, - I cm = m kg from equation. CiB) & ciu), weget. mase = mgsino -lismg cosa, from eq? cvi) moQ = mg sino - Usmg coso. Td = g sino - Usg cosa . Now, from eancu), weget. Yils rmy coso + els cose = sino Icm

Ms. Componente .. ceso sing ---- 2 a tano aus Imr< L Icm J S tancee üst o = tant Los ton (une femme #17 == tari oz{ Comp) +] - 53. 5117 to = 53.511 ie, 10= 5 3.Sil ~Cons)