Does changing radius or speed affect centripetal acceleration?

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SUMMARY

Changing the speed and radius significantly affects centripetal acceleration, which is defined by the formula \( a_c = \frac{v^2}{r} \). Doubling the speed results in a fourfold increase in centripetal acceleration when the radius remains constant. Conversely, doubling the radius while keeping speed constant halves the centripetal acceleration. The dependence on speed is quadratic, while the dependence on radius is linear, indicating that speed has a stronger influence on centripetal acceleration.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula
  • Familiarity with basic physics concepts such as speed and radius
  • Knowledge of non-linear relationships in physics
  • Ability to perform simple mathematical calculations
NEXT STEPS
  • Explore the derivation of the centripetal acceleration formula \( a_c = \frac{v^2}{r} \)
  • Investigate the effects of varying radius and speed on circular motion
  • Learn about the implications of non-linear relationships in physics
  • Conduct experiments or simulations to visualize centripetal acceleration changes
USEFUL FOR

Students studying physics, educators teaching circular motion concepts, and anyone interested in the dynamics of motion in circular paths.

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Does changing the radius or changing the speed affect centripetal accelereation more? Why?
 
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Welcome to PF,

HOW does the centripetal acceleration depend on the speed and radius? If this is homework, it should be posted in the homeowork help section, whose posts have a template that forces you to include helpful things like *relevant equations* and your attempt at a solution (things that are helpful to YOU for arriving at a solution).

So, try varying each parameter and seeing what happens. If you double the speed, what happens to the centripetal acceleration (keeping the radius constant)? How about if you double the radius (keeping the speed constant)? On which variable does the acceleration seem to have a stronger dependence, the speed, or the inverse of the radius? (Hint: it's pretty obvious because one of them is a non-linear dependence)
 
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