A block of mass m is kept on a horizontal ruler. The friction coefficient between the ruler and the block is μ. The ruler is fixed at one end and the block is at a distance L from the fixed end. The ruler is rotated about the fixed end in the horizontal plane through the fixed end. If the angular speed of the ruler is uniformly increased from zero at an angular acceleration α, at what angular speed will the block slip?
It has a radial acceleration of ω2 L and a tangential acceleration of α L.
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∴ Its magnitude of net acceleration ,anet=√ω4L2+α2L2
As friction is the force that provides this acceleration,
f=m√ω4L2+α2L2
Now, for more value of ω , f = μN
μN=m√ω4L2+α2L2
⇒μmg=m√ω4L2+α2L2
⇒μg=√ω4L2+α2L2
⇒μ2g2=ω4L2+α2L2
⇒ω=[(μgL)2−α2]14