Final answer:
To find the rotational speed at which the coin slides off, we can calculate the maximum static friction force, torque, and angular acceleration and then use these values to find the rotational speed.
Step-by-step explanation:
To find the rotational speed at which the coin slides off, we need to consider the maximum static friction force that can act on the coin. The maximum static friction force is given by the coefficient of static friction multiplied by the normal force. The normal force can be calculated as the weight of the coin, which is equal to the mass of the coin multiplied by the acceleration due to gravity. Using these values, we can find the maximum static friction force.
Next, we can use the maximum static friction force to find the torque required to overcome the static friction. The torque is calculated as the product of the maximum static friction force and the distance of the coin from the center of the turntable. Using the torque, we can find the angular acceleration of the turntable.
Finally, we can use the angular acceleration to find the rotational speed at which the coin slides off. The rotational speed is the square root of the product of the angular acceleration and the distance of the coin from the center of the turntable.