find the linear speed of each point 2cm and 15cm from the axis of a phonograph record rotating at 33 and 1/3 rev/min

Your School Subject is the University of Liberia? Are you studying the history of the school, it's governance, its students and faculty? I'm sure it's interesting, but fail to see how a phonograph record has anything to do with the study of an institution. If you are studying physics, you might want to put that in the School Subject line/box so a physics tutor might see your question.

for 2 cm, r=2. So, just figure the circumference of the circle of radius 2...

100/3 rev/min * 2π*2 cm/rev = 400π/3 cm/min

similarly for r=15.

To find the linear speed of each point on the phonograph record, we need to convert the rotational speed from revolutions per minute (rpm) to radians per second (rad/s). Once we have the rotational speed in rad/s, we can use the formula for linear speed to calculate it.

First, let's convert the rotational speed from rpm to rad/s. Since 1 revolution is equal to 2π radians, we can use the following conversion factor:

1 rev/min = (2π rad/1 rev) × (1 min/60 s) = π/30 rad/s

Given that the phonograph record is rotating at 33 and 1/3 rev/min, the rotational speed in rad/s is:

33 1/3 rev/min × π/30 rad/s = (100/3)π/30 rad/s ≈ 3.333π/30 rad/s

Now, we can calculate the linear speed of each point on the phonograph record. The formula for linear speed is:

Linear Speed = Radius × Angular Speed

For the point 2 cm from the axis, the radius is 2 cm or 0.02 m. The angular speed is approximately 3.333π/30 rad/s.

Linear Speed = 0.02 m × (3.333π/30 rad/s) = (0.02 × 3.333π/30) m/s ≈ 0.00694π m/s ≈ 0.02181 m/s

So, the linear speed of the point 2 cm from the axis is approximately 0.02181 m/s.

For the point 15 cm from the axis, the radius is 15 cm or 0.15 m. The angular speed is still approximately 3.333π/30 rad/s.

Linear Speed = 0.15 m × (3.333π/30 rad/s) = (0.15 × 3.333π/30) m/s ≈ 0.04996π m/s ≈ 0.157 m/s

So, the linear speed of the point 15 cm from the axis is approximately 0.157 m/s.