A 20 kg block is 1 m from the axis of a turntable starting from rest with angular acceleration 3 rad/s². The friction coefficient is 0.5. At t=x/3 s the block is just about to slip. Find x.
Physics · Circular Motion · friction and circular motion
JEE Advanced

Question

A 20 kg block is 1 m from the axis of a turntable starting from rest with angular acceleration 3 rad/s². The friction coefficient is 0.5. At t=x/3 s the block is just about to slip. Find x.

G1 Physics · Accepted Answer

At impending slip, friction must provide radial acceleration ω²R and tangential acceleration αR, so (µg)²=ω⁴R²+α²R². With µg=5, R=1 and α=3, 25=ω⁴+9, hence ω=2 rad/s. Since ω=αt=3(x/3)=x, x=2.