Question

(a) What is the angular velocity (rad/s) of the platter of the hard drive rotating at 7200 rpm?

A. 753.98 rad/s
B. 753.98 rev/s
C. 120π rad/s
D. 120π rev/s

(b) If the reading head is located 3.00 cm from the rotation axis, what is the linear speed of the point on the platter just below it?
A. 180 m/s
B. 360 m/s
C. 540 m/s
D. 720 m/s

(c) If a single bit requires 0.50 μm of length along the direction of motion, how many bits per second can the writing head write when it is 3.00 cm from the axis?
A. 2.15 × 10^8 bits/s
B. 4.30 × 10^8 bits/s
C. 6.45 × 10^8 bits/s
D. 8.60 × 10^8 bits/s

Answer 1

The angular velocity of a hard drive platter rotating at 7200 rpm is 120π rad/s. Calculating the linear speed gives 3.6π m/s or approximately 11.31 m/s for a point 0.03 m from the center. The number of bits per second that can be written under these conditions is approximately 2.262 × 107 bits/s, which does not match provided answer choices.

Step-by-step explanation:

To address the questions provided, we need to perform calculations based on formulas that relate angular velocity, linear speed, and acceleration in rotational motion. The formulas we will use include conversions between revolutions per minute (rpm) and radians per second for angular velocity, and then using that to find linear speed and acceleration.

Angular Velocity Calculation

To convert rpm to radians per second, we use the conversion ratio: 1 rev = 2π radians and 1 minute = 60 seconds. Therefore, the angular velocity (ω) in radians per second for a hard drive spinning at 7200 rpm is:

ω = 7200 rpm × (2π rad/rev) × (1 min/60 s) = 120π rad/s.

Linear Speed Calculation

The formula for linear speed (v) is: v = rω, where r is the radius. For a reading head located 3.00 cm from the rotation axis (0.03 m), the linear speed at this point on the platter is:

v = 0.03 m × 120π rad/s = 3.6π m/s, which is approximately 11.31 m/s (not matching any provided answer choices).

Bits Per Second Calculation

To calculate the number of bits written per second, consider the length each bit takes along the platter's surface and the linear speed. The calculation is:

Number of bits/s = Linear speed / Length per bit. Assuming a linear speed of 11.31 m/s (as calculated previously) and a bit length of 0.50 μm (0.50 × 10-6 m), we have:

Number of bits/s = 11.31 m/s / (0.50 × 10-6 m/bit) = 2.262 × 107 bits/s (also not matching any provided answer choices).

It should be noted that the provided answer choices for the linear speed and bits per second do not correspond to the calculations performed with the provided data. Thus, there might be a misunderstanding or misprint in the question or answer choices.