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dv/dt = a
Now, at every instant before slipping the frictional force f equals the resultant of centripetal and tangential forces
f2 = (mv2/R)2 + (m(dv/dt))2
For no slipping,
f<  N
(mv2/R)2 + (m(dv/dt))2 <( mg)2
(v2/R)2 + a2 <2g2
v < [(2g2 - a2 )R2]1/4
Hence the speed at which the car slips
v = [(2g2 - a2 )R2]1/4
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Moderation Team
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