Final answer:
Typical hard disk speeds include 5400 rpm and 7200 rpm, and calculations in rotational motion apply principles such as angular acceleration and revolutions to determine behavior of objects like gyroscopes, CDs, and compact discs.
Step-by-step explanation:
Understanding Rotational Speed and Kinematics
The typical rotational speeds for a hard disk in a computer are often 5400 rpm and 7200 rpm. High-performance drives may run at 10000 rpm or more. This speed is crucial in determining how fast a computer can access and transfer data.
To address the rotational motion questions, we can apply the kinematics of rotational motion. For instance:
- Angular acceleration can be found using the formula α = Δω / Δt, where δω is the change in angular velocity and Δt is the change in time.
- The number of revolutions a rotating object goes through can be calculated by the total angle rotated in radians divided by 2π radians (since there are 2π radians in one revolution).
- To find the total distance traveled by a point on a rotating object, like a piece of dust on a CD, one would multiply the circumference of the path (2πr) by the number of revolutions it makes.
Let's calculate a specific example:
- If a gyroscope is accelerated from rest to 32 rad/s in 0.40 s, its angular acceleration is 32 rad/s divided by 0.40 s, which equals 80 rad/s².
- The number of revolutions it goes through in the process can be found by integrating the angular velocity over time to find the total angle, and then dividing by 2π. The piece of dust on a spinning CD at 500 rpm for 3 minutes (180 seconds), located 4.3 cm from the center will travel a distance of 2π(0.043m) * (500/60 * 180), assuming a constant rotational speed without considering the startup phase.
When it comes to objects like a compact disc or a hovercraft fan, we analyze their rotational motion using the same principles of angular velocity, angular acceleration, and the distances traveled along a circular path.