Modern hard drives spin very fast! The part that holds the data is a disk called the platter. Assume an aluminum platter that is 3.5in in diameter, 1 mm thick, and spinning at 5400 rpm . Treat the platter as a solid disk - don't worry about the hole in the middle.
To calculate the linear speed of the outer edge of the platter, we can use the formula:
v = ωr
Where:
v is the linear speed
ω (omega) is the angular velocity in radians per second
r is the radius of the platter
First, let's convert the rotational speed from RPM to radians per second:
ω = (2π × RPM) / 60
Plugging in the given values:
ω = (2π × 5400) / 60
= 2π × 90
= 180π rad/s
Now, let's calculate the radius of the platter. Since the diameter is given, we can divide it by 2 to get the radius:
r = 3.5in / 2
= 1.75in
To convert this to meters (SI unit), we'll multiply by 0.0254:
r = 1.75in × 0.0254m/in
= 0.04445m
Now, let's calculate the linear speed of the outer edge:
v = ωr
= 180π rad/s × 0.04445m
≈ 282.743 m/s
Therefore, the linear speed of the outer edge of the platter is approximately 282.743 m/s.