A student puts on a Dresden Dolls disc in her cd player which spins at 1800 revolutions per minute. A compact disc has a mass of about 0.016 kg and a radius of 6.0 cm.

a) What is the period of rotation in seconds?

b) What is the frequency of the rotating disc?

c) What is the angular speed of the disc?

d) What is the linear speed of a scratch on the outer edge of the disc?

a. T=1min/1800rev=60s/1800rev=0.0333 s.

b. F = 1/T = 1/0.0333 = 30 cy/s = 30 Hz.

c. Va=30cy/s * 6.28rad/cy=188.84 rad/s.
= Angular velocity.

d. C = pi*2r = 3.14*12 = 37.7 cm = 0.377 m = The Circumference.

V = 30cy/s * 0.377m/cy = 11.3 m/s.

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 = (2π * 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.