a coin placed on a disc rotates with speed of 33 1/3 rev. per minute provided that the coin is no more than 10 cm from the axis calculate the coefficient of static friction between the coin and the disc

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A coin placed on a disc

Good

To calculate the coefficient of static friction between the coin and the disc, we need to use the concept of centripetal force.

1. First, we need to determine the centripetal force acting on the coin. The centripetal force required to keep the coin in circular motion can be calculated using the formula:

Fc = (m * v^2) / r

Where Fc is the centripetal force, m is the mass of the coin, v is the linear velocity (converted from the given rotational speed), and r is the radius of the circular path (which is the distance of the coin from the axis).

2. We need to convert the rotational speed of 33 1/3 revolution per minute to linear velocity. One revolution is equivalent to 2π radians, and the time taken for one revolution is 1/revolutions per minute. We can use this information to calculate the linear velocity:

v = (2π * r * revolutions per minute) / 60

Given that revolutions per minute is 33 1/3, we can convert it to a decimal by dividing 1 by (1/3), and substitute the values into the formula.

3. Use the radius of the circular path, which is given as 10 cm, and convert it to meters by dividing by 100.

r = 10 cm / 100

4. Determine the mass of the coin, as it is not given in the question.

5. Substitute the calculated values into the centripetal force formula to get the value of the centripetal force.

6. The coefficient of static friction (μs) between the coin and the disc can be calculated using the formula:

Fs = μs * N

Where Fs is the static frictional force and N is the normal force.

7. In this case, the normal force is equal to the weight of the coin, which can be calculated using the formula:

N = m * g

Where g is the acceleration due to gravity.

8. Substitute the weight (m * g) and the calculated centripetal force (Fc) into the formula for static friction to get the desired coefficient of static friction (μs).

Note that without knowing the mass of the coin, it is not possible to calculate the coefficient of static friction accurately.