A CD has to rotate under the readout-laser with a constant linear velocity of 1.25 m/s. If the laser is at a position 3.2 cm from the center of the disk, what are the revolutions per minute (rpms) of the disk?
To find the revolutions per minute (rpms) of the disk, we can use the formula:
rpm = (linear velocity / circumference) * 60
First, we need to calculate the circumference of the disk. The circumference of a circle can be given by the formula:
circumference = 2 * π * radius
Given that the laser is at a position 3.2 cm from the center of the disk, we can calculate the radius:
radius = 3.2 cm = 0.032 m
Now, we can calculate the circumference:
circumference = 2 * π * 0.032 m
Next, we can substitute the values into the rpm formula:
rpm = (1.25 m/s / (2 * π * 0.032 m)) * 60
Simplifying further:
rpm = (1.25 / (2 * 3.14 * 0.032)) * 60
rpm ≈ 118.78
Therefore, the revolutions per minute (rpms) of the disk would be approximately 118.78 rpms.
To determine the revolutions per minute (rpms) of the disk, we can use the relationship between linear velocity and angular velocity. The linear velocity is given as 1.25 m/s, and we're asked to find the angular velocity in rpms.
First, let's convert the given linear velocity from m/s to cm/s since the position of the laser is given in centimeters. We know that 1 m = 100 cm, so 1.25 m/s is equal to 125 cm/s.
Next, let's determine the circumference of the disk at the position of the laser. The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius. In this case, the radius is the distance from the center of the disk to the laser position, which is 3.2 cm.
Using the formula C = 2πr, we can calculate the circumference:
C = 2π(3.2 cm) = 6.4π cm
Now, we can find the angular velocity in radians per second (rad/s) using the formula:
Linear Velocity = Angular Velocity × Circumference
Substituting the values, we have:
125 cm/s = Angular Velocity × 6.4π cm
To get the angular velocity, we rearrange the formula:
Angular Velocity = 125 cm/s / (6.4π cm)
Simplifying this expression, we have:
Angular Velocity = 19.64 rad/s (approximately)
Finally, to convert the angular velocity from rad/s to rpms, we know that 1 revolution is equal to 2π radians. Therefore, 1 rad/s is equivalent to (1/2π) rpms.
Converting the angular velocity of 19.64 rad/s to rpms, we have:
Angular Velocity in rpms = 19.64 rad/s × (1/2π) rpms/rad ≈ 1.97 rpms
Therefore, the disk is rotating at approximately 1.97 rpms.