Answer:
81 mm from the center
Explanation:
5.67g = 0.00567 kg
33.3 revolutions per minute = 33.3 (rev/min) * 2Ï€ (rad/rev) * (1/60) (min/sec) = 3.487 rad/s
The weight of the coin is product of mass and gravitational acceleration g = 9.81m/s2
W = mg = 0.00567 * 9.81 = 0.0556 N
Which is also the normal force of the record acting back on the coin to balance it.
Them the static friction is product of normal force and friction coefficient
[tex]F_f = N\mu = 0.0556*0.1 = 0.00556 N[/tex]
For the coin to NOT slip off, its centripetal force should at most be equal to the static friction
[tex]F_c = 0.00556[/tex]
[tex]a_cm = 0.00556[/tex] Newton's 2nd law
[tex]a_c = 0.00556 / 0.00567 = 0.981 m/s^2[/tex]
The centripetal acceleration is the product of squared angular velocity and radius of circular motion
[tex]a_c = \omega^2r[/tex]
[tex]r = \frac{a_c}{\omega^2} = \frac{0.981}{3.487^2} = 0.081m[/tex] or 81 mm
