Question

14. A particle is detached from the rim of a rotating disc of radius 70 cm and angular frequency 30 rpm. The disc is situated 2.5 m above the
horizontal floor. The horizontal distance covered by particle before hitting the floor: (answer in meter)​

Answer 1

$\huge\red{Answer}$

The angular displacement of the particle till it attains velocity ω is 

θ=2αω2−ω02

Where ω=0 (because the particle starts from rest)

Then θ=2αω2−ω02..................(i)

Let us calculate ω

The total acceleration of the particle is 

a=a12+ar2

Where at=Rαandar=Rω2

If the maximum acceleration of the particle is a0 we have 

a0=R2α2+R2ω4

This given ω=(2Rαa02−R2θ2)41