Moment of Inertia and Angular Speed

Click For Summary
SUMMARY

The discussion focuses on calculating the angular speed of a top with a moment of inertia of 4.40 x 10-4 kgm2 after 80.0 cm of string is unwound under a constant tension of 5.19 N. The key concept is the work done by the string, which translates into a change in kinetic energy. Using the equation ΔK = 0.5I(ωfinal2 - ωinitial2), participants derive the final angular velocity based on the work-energy principle.

PREREQUISITES
  • Understanding of moment of inertia and its significance in rotational dynamics.
  • Familiarity with the work-energy theorem in physics.
  • Knowledge of angular velocity and its relationship with rotational motion.
  • Basic algebra for manipulating equations involving kinetic energy.
NEXT STEPS
  • Study the work-energy theorem in rotational motion.
  • Learn how to calculate angular momentum and its conservation.
  • Explore the relationship between torque, angular acceleration, and moment of inertia.
  • Investigate practical applications of rotational dynamics in engineering contexts.
USEFUL FOR

Physics students, educators, and anyone interested in understanding rotational dynamics and energy transformations in mechanical systems.

TrippingBilly
Messages
27
Reaction score
0
A top has a moment of inertia of 4.40 10-4 kgm2 and is initially at rest. It is free to rotate about the stationary axis AA'. A string, wrapped around a peg along the axis of the top, is pulled in such a manner as to maintain a constant tension of 5.19 N. If the string does not slip while it is unwound from the peg, what is the angular speed of the top after 80.0 cm of string has been pulled off the peg? (The picture of the top shows it rotating clockwise about a vertical axis A)

This question has me stumped. If someone could point me in the right direction with regards to a concept I need to know or something I would appreciate it.
 
Physics news on Phys.org
Hint: How much work is done by the string?
 
At first I didn't see where you were going, but then I realized that work = change in energy. Which enabled me to use that wonderful equation
delta K = .5I(final angular velocity^2 - initial angular velocity^2). Thanks for the hint!
 

Similar threads

Angular Momentum Problem: Mouse walking on a rotating turntable
  • · Replies 5 ·
Replies
5
Views
2K
Moment of Inertia: Disk 1 & 2 Homework
  • · Replies 1 ·
Replies
1
Views
2K
How Does Adding Masses Affect the Angular Velocity of a Rotating Cylinder?
  • · Replies 12 ·
Replies
12
Views
3K
Simple Ice Skater with Conservation of Angular Momentum
  • · Replies 4 ·
Replies
4
Views
2K
Ideal Vs Real Mass Pulley system
  • · Replies 10 ·
Replies
10
Views
5K
What is the angular acceleration of the rod?
  • · Replies 18 ·
Replies
18
Views
7K
A Spinning Top and Rotation Dynamics
  • · Replies 8 ·
Replies
8
Views
8K
Angular acceleration of plank hanging off edge with a weight
  • · Replies 7 ·
Replies
7
Views
2K
What Happens to Angular Acceleration and Moment of Inertia in a Pulley System?
  • · Replies 2 ·
Replies
2
Views
8K
Calculating Angular Speed of Rotating Apparatus with Attached Mass and Rod
  • · Replies 1 ·
Replies
1
Views
2K