A small particle of mass 0.36 g rests on a horizontal turntable at a distance 25 cm from the axis of spindle. The turntable is accelerated at a rate of α = 3 1 rad / s 2 . The frictional force that

Question

A small particle of mass 0.36 g rests on a horizontal turntable at a distance 25 cm from the axis of spindle. The turntable is accelerated at a rate of α = 3 1 ​ rad / s 2 . The frictional force that the table exerts on the particle 2 s after the startup is

TestHub · Accepted Answer

Friction supplies both components: f = m a t 2 ​ + a r 2 ​ ​ = m ( R α ) 2 + ( R ω 2 ) 2 ​ with ω = α t . At t = 2 s : R α = 12 1 ​ m / s 2 and R ω 2 = 0.25 × 9 4 ​ = 9 1 ​ m / s 2 . So f = 0.36 × 1 0 − 3 × 144 1 ​ + 81 1 ​ ​ = 0.36 × 1 0 − 3 × 0.139 ​ = 50 × 1 0 − 6 N = 50 μ N . ​

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