To find the answers to these questions, we need to use some formulas related to rotational motion.
a) The period of rotation is the time it takes for the CD to complete one revolution. It can be calculated using the formula:
Period = 1 / (Revolutions per minute)
First, let's convert the revolutions per minute (rpm) to revolutions per second by dividing it by 60.
Revolutions per second = 1800 rpm / 60 = 30 revolutions per second
Now, we can calculate the period:
Period = 1 / 30 = 0.0333 seconds
So, the period of rotation is 0.0333 seconds.
b) The frequency of the rotating disc is the number of revolutions per unit of time. It is the reciprocal of the period:
Frequency = 1 / Period
Frequency = 1 / 0.0333 = 30 Hz
So, the frequency of the rotating disc is 30 Hz.
c) The angular speed of the disc is the rate at which the disc rotates in radians per unit of time. It can be calculated using the formula:
Angular speed = (2Ï€ * Revolutions per minute) / 60
First, let's convert the revolutions per minute to radians per second:
Revolutions per second = 1800 rpm / 60 = 30 revolutions per second
Now, we can calculate the angular speed:
Angular speed = (2π * 30) / 60 = π radians per second
So, the angular speed of the disc is π radians per second.
d) The linear speed of a scratch on the outer edge of the disc can be calculated using the formula:
Linear speed = (Angular speed) * (Radius)
Linear speed = π * (6.0 cm) = 18.84 cm/s
So, the linear speed of a scratch on the outer edge of the disc is 18.84 cm/s.