A coin is placed 26 cm from the center of a horizontal turntable, initially at rest. The turntable then begins to rotate. When the speed of the coin is 120 cm/s (rotating at a constant rate), the coin just begins to slip. The acceleration of gravity is 980 cm/s

2.
What is the coefficient of static friction between the coin and the turntable?

To find the coefficient of static friction between the coin and the turntable, we can use the following equation:

Centripetal force = Static friction force

The centripetal force acting on the coin is provided by the friction force between the turntable and the coin. This force can be calculated using the formula:

Centripetal force = (mass of the coin) x (centripetal acceleration)

The mass of the coin is not provided, but we can calculate it using the given information. The centripetal acceleration of the coin is given by the formula:

Centripetal acceleration = (velocity of the coin)^2 / (radius of the turntable)

Given:
Velocity of the coin (v) = 120 cm/s
Radius of the turntable (r) = 26 cm

Let's calculate the centripetal acceleration first:

Centripetal acceleration = (120 cm/s)^2 / 26 cm
Centripetal acceleration = 57600 cm^2/s^2 / 26 cm
Centripetal acceleration = 2215.38 cm/s^2

Now, we can calculate the mass of the coin:

Centripetal force = (mass of the coin) x (centripetal acceleration)
Static friction force = (mass of the coin) x (centripetal acceleration)

Since the coin is not slipping, the static friction force can be represented as:

Static friction force = (coefficient of static friction) x (normal force)

The normal force is equal to the weight of the coin, which can be calculated using the formula:

Weight of the coin = (mass of the coin) x (acceleration due to gravity)

Given:
Acceleration due to gravity (g) = 980 cm/s^2

Let's calculate the weight of the coin:

Weight of the coin = (mass of the coin) x (acceleration due to gravity)
Weight of the coin = (mass of the coin) x (980 cm/s^2)

Now, we know that the static friction force is equal to the centripetal force, so we can equate the two equations:

Static friction force = (coefficient of static friction) x (normal force)
Static friction force = (mass of the coin) x (centripetal acceleration)

Now we can substitute the equations with the values we've calculated:

(coefficient of static friction) x (mass of the coin) x (980 cm/s^2) = (mass of the coin) x (2215.38 cm/s^2)

Now, we can cancel out the mass of the coin from both sides of the equation:

(coefficient of static friction) x (980 cm/s^2) = 2215.38 cm/s^2

Finally, let's solve for the coefficient of static friction:

Coefficient of static friction = 2215.38 cm/s^2 / 980 cm/s^2

Coefficient of static friction ≈ 2.26

never mind, i got it.