A coin is placed on an old record turntable which rotates at 78 rpm. The coefficient of friction between the record and the coin is 0.17.

a) What is the angular speed of record in radians/s?
b) At what distance (m) from the center will the coin begin to slide off the record?
c) What is the period of the rotation (s) of the penny?

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a) To find the angular speed of the record in radians per second, we need to convert the given value of 78 rpm into radians per second.

The conversion factor to convert from rpm (revolutions per minute) to radians per second is:
1 rpm = 2π radians/60 seconds

So, the angular speed of the record in radians per second is:
Angular speed = 78 rpm * (2π radians/60 seconds)
= (78 * 2π) / 60
= 2.58 radians/second

b) To determine at what distance from the center the coin will begin to slide off the record, we need to consider the maximum friction force that can prevent sliding.

The maximum friction force can be calculated using the formula:
Friction force (F) = coefficient of friction (μ) * Normal force (N)

The normal force acting on the coin is equal to the weight of the coin, which is the force of gravity acting on the coin. The weight of the coin can be calculated using the equation:
Weight (W) = mass (m) * acceleration due to gravity (g)

First, we need to determine the mass of the coin in order to calculate its weight. Once we have the weight, we can use it to find the normal force acting on the coin.

c) The period of the rotation of the penny can be calculated using the formula:
Period (T) = 1 / Frequency (f)

The frequency is the number of revolutions per second, which can be found by dividing the angular speed (in radians per second) by 2π.