An old record player of `15.0 cm` radius at `33.0"rev" min^(1)` while mounted on a `30^(@)` incline as shown in figure

a. If a mass `m` can be placed anywhere on the rotaing record , where is the most critical place on the disc where slipping might occur ?
b.Calculate the least possible coefficient of friction that must exist if no slipping occurs.

Explanation

a. Rim
b. Maximum friction is required at bottom most point as `mu` calculate here will be the least value repaired

`f ge mg sin theta + m omega^(2)r`
`mu mg cos theta ge mg sin theta + m omega^(2) r`
`muge tan theta + (omega^(2)r)/(g cos theta) = (1)/(sqrt(3)) + ( 4 pi^(2) xx 1089 xx 30)/(3600 xx 1000 xx sqrt(3))`
` = (1)/(sqrt(3))+ (4 pi^(2) xx 363)/(4 sqrt(3) xx 1000)`
`= (1)/(sqrt(3)) [(1 + (pi^(2) xx 363)/(10.000))]`