Brian L. answered 11/25/19
Pharmacist specializing in many areas of math and science
Let ω = angular speed = 1.7 rev s-1 = 3.4π rad s-1
Let r = distance from the coin to the axis of rotation = 14.6 cm = 0.146 m
Let vt = tangential speed = rω = (0.146 m)(3.4π rad s-1)
Let ac = centripetal acceleration = rω2 = (0.146 m)(3.4π rad s-1)2 =
The coin will slide off the turntable when the centripetal force (Fc) exceeds the force of static friction (Ff).
The centripetal force is calculated as:
Fc = mac = (67 g)(0.146 m)(3.4π rad s-1)2(10-3 kg g-1)(1 N kg-1 m-1 s2) = 1.12 N
The formula for the force of static friction is:
Ff = µsFN, where µs is the coefficient of static friction and FN is the normal force.
The normal force is the force exerted on the coin by the surface of the turntable. It is equal in magnitude and opposite direction to the weight of the coin:
FN = mg
We can now solve for the coefficient of static friction by setting Ff equal to Fc:
µsFN = µsmg = mac
µsg = ac
µs = g ÷ ac = (9.81 m s-2) ÷ 16.66 m s-2 = 0.59