A coin of mass 0.01 kg is placed a distance 5 cm from the center of a phonograph turntable. The coefficient of static friction is 0.25. The rotational speed ⍵ of the turntable is slowly increased until the coin slides off. What is this rotational speed (in rad/s) when the coin slides off?

rotational speed is w = 0.35 rad/s

Explanation:

Let's analyze the exercise a little, we have the phonograph movement that rotates the constant angular velocity, so that the speed of the body is constant, note that the speed is the scalar, but the speed does change as the direction changes

Since it is a circular motion we can find the centripetal acceleration

a = v² / R

v = w R

a = w² R

Having the acceleration of the currency let's use Newton's second law

-fr = m a

N-W = 0 ⇒ N = W

fr = μ N

Calculate

μ (mg) = m (w² R)

μ g = w² R

w = √ μgR

w = √ 0.25 9.8 0.05

w = 0.35 rad / s