The hard disk in a laptop computer contains a small disk that rotates at a rate of 5000 rpm. If this disk has a radius of 2.3 cm, what is the centripetal acceleration of a point at the edge of the disk?_____m/s^2

To find the centripetal acceleration at the edge of the disk, you can use the formula:

ac = ω^2 * r

where "ac" represents the centripetal acceleration, "ω" is the angular velocity, and "r" represents the radius.

First, let's convert the rotation rate from revolutions per minute (rpm) to radians per second (rad/s). Since there are 60 seconds in a minute, we can calculate:

ω = (5000 rpm) * (2π rad/1 rev) * (1 min/60 s)

Simplifying this equation, we get:

ω = (5000 * 2 * π) / 60 rad/s
= 523.60 rad/s

Now we can substitute the values into the formula to calculate the centripetal acceleration:

ac = (523.60 rad/s)^2 * 2.3 cm

However, it is important to convert the radius from centimeters to meters, as the SI unit of acceleration is meters per second squared (m/s^2). There are 100 centimeters in a meter, so:

ac = (523.60 rad/s)^2 * (2.3 cm / 100)
= (523.60 rad/s)^2 * 0.023 m

Calculating this equation, we find:

ac = 138,090.952 m/s^2

Therefore, the centripetal acceleration of a point at the edge of the disk is approximately 138,090.952 m/s^2.