A small particle of mass 0.72 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 0.72 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

​ ω = α t = 3 1 ​ × 2 = 3 2 ​ rad / s , a t ​ = R α = 0.25 × 3 1 ​ = 12 1 ​ m / s 2 , a r ​ = R ω 2 = 0.25 × ( 3 2 ​ ) 2 = 9 1 ​ m / s 2 , so a = a t 2 ​ + a r 2 ​ ​ = 144 1 ​ + 81 1 ​ ​ = 36 5 ​ ≈ 0.139 m / s 2 and f = ma = 0.72 × 1 0 − 3 × 0.139 = 100 × 1 0 − 6 N = 100 μ N . ​

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