Rotational Motion: The Relationship Between Linear and Angular Displacement

Click For Summary
In rotational motion, when a mass attached to a rope falls a distance x meters, the string must also move through x meters around the rim or disk. This relationship can be expressed mathematically as s = rθ, where s is the linear displacement, r is the radius, and θ is the angular displacement in radians. The discussion emphasizes that the linear distance fallen by the mass directly correlates to the angular distance traveled by the rim or disk. This connection highlights the conservation of distance in the system. Understanding this relationship is crucial for analyzing rotational dynamics effectively.
ehabmozart
Messages
212
Reaction score
0
Suppose a mass attached to a rope which winds around a rim or a disk. If the mass attached to the string falls x meters, should the string also move thorugh x meters around the rim or the disk which we can relate by s = r theta?
 
Physics news on Phys.org
Yes, it pretty much has to doesn't it? That "x" distance has to come from somewhere!
 

Thread 'Mousetrap Car Energy efficiency'

For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...
View full post »

Similar threads

Undergrad Writing an equation for torque around an arbitrary point on a body
  • · Replies 6 ·
Replies
6
Views
1K
High School Rotational Dynamics: Confused about the tension in this string pulling a mass up an incline
  • · Replies 2 ·
Replies
2
Views
2K
High School Rolling Motion Test: Take the Challenge and Justify Your Answers
  • · Replies 37 ·
2
Replies
37
Views
4K
Undergrad Equation of motion for a simple mechanical system
  • · Replies 2 ·
Replies
2
Views
2K
How Does Mass Affect the Direction of Rotational Motion in a Pulley System?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How can angular displacement be larger than 2pi?
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Velocity transformation between frames rotating relative to one another
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Equations of Motion for Torsional Inverted Pendulum on a moving cart
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Rigid body motion (RBM) transformation
  • · Replies 3 ·
Replies
3
Views
1K
Observation about the rotation of a disc
  • · Replies 4 ·
Replies
4
Views
1K