Questions: Hard disks are circular disks that store data in your computer. Suppose a circular hard disk is 3.5 inches in diameter. If the disk rotates at 7100 revolutions per minute, what is the linear speed of a point on the edge of the disk (in inches per minute)? The linear speed is approximately inches per minute. (Do not round until the final answer. Then round to two decimal places as needed.)

Solution Steps

To find the linear speed of a point on the edge of the disk, we need to calculate the circumference of the disk and then multiply it by the number of revolutions per minute. The circumference of a circle is given by the formula \( C = \pi \times \text{diameter} \). Once we have the circumference, we multiply it by the number of revolutions per minute to get the linear speed.

The circumference \( C \) of a circular disk is given by the formula: \[ C = \pi \times \text{diameter} \] Substituting the diameter of the disk: \[ C = \pi \times 3.5 \approx 10.9956 \text{ inches} \]

The linear speed \( v \) of a point on the edge of the disk can be calculated by multiplying the circumference by the number of revolutions per minute: \[ v = C \times \text{revolutions per minute} \] Substituting the values: \[ v = 10.9956 \times 7100 \approx 78068.5774 \text{ inches per minute} \]

Rounding the linear speed to two decimal places gives: \[ v \approx 78068.58 \text{ inches per minute} \]

Final Answer