Question

A computer hard drive contains a circular disk with diameter 2.5 inches and spins at a rate of 7200 RPM (revolutions per minute). Find the linear speed of a point on the edge of the disk in miles per hour.

Answer 1

The linear speed of a point on the edge of the disk is 66.37 miles per hour.

Step-by-step explanation:

The linear speed of a point on the edge of the disk can be calculated using the formula:

v = π * d * n

where:

• v is the linear speed
• d is the diameter of the disk
• n is the number of revolutions per minute

Plugging in the values, we have:

v = π * 2.5 inches * 7200 RPM

Converting inches to miles and minutes to hours, the linear speed can be calculated as:

v = (π * 2.5 * 7200 * 60) / (12 * 5280)

Simplifying the expression, the linear speed of a point on the edge of the disk is approximately 66.37 miles per hour.

Answer 2

Now to solve this problem, all we have to remember is the formula for calculating the linear speed given the radial speed, that is:

v = r w

where,

v = is the linear velocity or linear speed

r = is the radius of the circular disk = (1 / 2) diameter = (1/ 2) (2.5 inches) = 1.25 inches

w = is the radial velocity (must be in rad per time) = 7200 rev per minute

Calculating for v:

v = 1.25 inches (7200 rev per minute) (2 π rad / 1 rev)

v = 56,548.67 inches / minute

Converting to miles per hour:

v = 56,548.67 inches / minute (1 mile / 63360 inches) (60 min / hour)

v = 53.55 mile / hour