What is the relationship between tangential and radial acceleration?

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SUMMARY

The relationship between tangential and radial acceleration is defined by their perpendicular nature in circular motion. In this scenario, the tangential acceleration (αt) is given as 2.00 rad/s², while the radius (r) is 112 m. The total acceleration can be calculated using the formula aTotal² = aTang² + aRad², where radial acceleration is influenced by tangential speed. This understanding is crucial for solving problems involving circular motion dynamics.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with angular acceleration concepts
  • Knowledge of centripetal force principles
  • Ability to apply kinematic equations in physics
NEXT STEPS
  • Study the derivation of the formula aTotal² = aTang² + aRad²
  • Learn about the effects of varying radius on radial acceleration
  • Explore practical applications of tangential and radial acceleration in real-world scenarios
  • Investigate the relationship between angular velocity and tangential speed
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Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators seeking to explain the concepts of tangential and radial acceleration.

De_Dre01
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Homework Statement


qRDU6E6.png


Homework Equations


αt = r α

The Attempt at a Solution


ωi = 0 rad/s
αt = 2.00 rad/s2
r = 112 m
θ = ? at a = 6.80 m/s2

I'm not exactly sure where to begin. Help is appreciated.
 
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You have two kinds of acceleration here. Assuming the batmobile doesn't slip on the road as it's turning (radius being a constant), the two accelerations are perpendicular (one is tangential, and the other is radial (centripetal force). So you can add them like: aTotal^2 = aTang^2 + aRad^2.
One top of that, the radial acceleration is dependent on the tangential speed, so it's dependent on tangential acceleration.
 

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