Rotational Motion: Average angular acceleration of a CD

Click For Summary
SUMMARY

The average angular acceleration of a compact disc (CD) during its 74-minute playing time is calculated using the formula α = (ωf - ωi) / Δt. Given the initial angular velocity (ωi) of 50 rad/s and the final angular velocity (ωf) of 21.6 rad/s, the correct calculation yields an average angular acceleration of -0.006 rad/s². The error in the initial submission was due to incorrect significant figures; the final answer must be presented with three significant figures as -0.00600 rad/s².

PREREQUISITES
  • Understanding of rotational motion concepts
  • Familiarity with angular velocity and angular acceleration
  • Knowledge of significant figures in scientific calculations
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the principles of rotational dynamics in physics
  • Learn how to apply the equations of motion for rotational systems
  • Explore the significance of significant figures in scientific reporting
  • Investigate the relationship between linear speed and angular velocity
USEFUL FOR

Students studying physics, particularly those focusing on rotational motion and angular dynamics, as well as educators seeking to clarify concepts related to angular acceleration.

adangerousdriver
Messages
3
Reaction score
1

Homework Statement


"A compact disc (CD) stores music in a coded pattern of tiny pits 10−7m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s."
"What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive."

rinside=.025m
routside=.058m
v=1.25m/s
Calculated from previous parts of this problem:
ωinside=50rad/s
ωoutside=21.6rad/s
t=74min=74*60s

Homework Equations


α=(ωfi)/(Δt)

The Attempt at a Solution


I figured average angular acceleration would be calculated by subtracting the initial angular velocity from the final and dividing by the time interval, so I plugged in and performed this calculation:

(21.6rad/s-50rad/s)/(74*60s-0s)

to get -0.006 rad/s2. This is online homework and it told me my answer is incorrect. I can't tell what I'm doing wrong. I've tried submitting both -0.006 and 0.006.
 
Physics news on Phys.org
Your given values have 3 significant figures. What you've submitted only has one.
 
  • Like
Likes   Reactions: adangerousdriver
gneill said:
Your given values have 3 significant figures. What you've submitted only has one.
Welp that fixed it. Thank you!
 
  • Like
Likes   Reactions: gneill

Similar threads

Replies
9
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 5 ·
Replies
5
Views
14K
Replies
20
Views
5K
Replies
5
Views
2K
Replies
15
Views
3K
  • · Replies 1 ·
Replies
1
Views
6K
  • · Replies 1 ·
Replies
1
Views
2K