Linear Velocity: When to Use S/t or R*w

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SUMMARY

The discussion clarifies the conditions under which to use the formulas for linear velocity: v = S/t and v = R*w. When provided with angular velocity (w) and radius (R), the formula v = R*w is applicable. Conversely, when given arc length (S) and time (t), the formula v = S/t should be used. It is established that as the radius (R) increases in a rotating object with constant angular velocity (w), the linear velocity (v) also increases due to the greater distance traveled.

PREREQUISITES
  • Understanding of angular velocity (w)
  • Knowledge of radius (R) in rotational motion
  • Familiarity with arc length (S)
  • Basic concepts of linear velocity (v)
NEXT STEPS
  • Study the relationship between angular velocity and linear velocity in circular motion
  • Explore practical applications of v = R*w in engineering contexts
  • Investigate the implications of varying radius on linear velocity in rotating systems
  • Learn about the effects of time (t) on linear velocity calculations
USEFUL FOR

Students in physics, engineers working with rotational dynamics, and anyone interested in understanding the principles of linear and angular velocity in motion.

Miike012
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Linear Velocity...

Homework Statement


When do I use
v = S/t
OR
v = R*w

s= arc length
w = angular velocity
t = time


Homework Equations





The Attempt at a Solution

 
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You use the formulas that use the information you are given!

If you are given an "angular velocity" or an "radius", R, then you use v= Rw. If you are given an actual length and time, then you use v= S/T.
 


the equation v = R*w shows that when you have a simple rotating object, and when w is constant (not changing), the linear velocity of the object (v) increases as you go further away from the origin (as R increases). As R increases, the object has to travel more but w is the same, so v must increase also.
 

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