How Does Acceleration Affect a Car's Tire Rotation and Speed?

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SUMMARY

The discussion focuses on calculating the angular acceleration of a car's tires given a linear acceleration of 0.75 m/s² and tire radius of 0.3 m. The relevant equations include Vt = rw for linear velocity and a = (wf - wi) / t for angular acceleration. The problem also explores the relationship between tangential and centripetal acceleration when a car travels at a constant speed of 20 mph around a corner. The key takeaway is that while the car maintains a constant speed, it experiences centripetal acceleration due to the change in direction.

PREREQUISITES
  • Understanding of angular motion and linear motion concepts
  • Familiarity with the equations of motion, specifically Vt = rw
  • Knowledge of acceleration types: tangential and centripetal
  • Basic proficiency in physics, particularly kinematics
NEXT STEPS
  • Calculate angular acceleration using the formula a = (wf - wi) / t
  • Explore the relationship between linear and angular velocity with Vt = rw
  • Investigate the effects of centripetal acceleration on vehicles navigating curves
  • Study the implications of tire size on vehicle dynamics and performance
USEFUL FOR

Physics students, automotive engineers, and anyone interested in the dynamics of vehicle motion and tire performance.

johnnyyy
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Homework Statement


If a car with 30.0 cm tires is accelerating at 0.75 m/s^2, what is the angular acceleration? How fast will the tires be spinning from rest if the car accelerates for 1.50 minutes? And finally how fast will that be linearly?
T=90 seconds
R=.3 m

Homework Equations


Vt=rw

a=wf-wi/t

W=ø/t


The Attempt at a Solution



Homework Statement


Will a car traveling at exactly 20 mph around a corner have a tangential acceleration? Centripetal acceleration? Explain.


Homework Equations





The Attempt at a Solution

 
Last edited:
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johnnyyy said:

Homework Statement


If a car with 30.0 cm tires is accelerating at 0.75 m/s^2, what is the angular acceleration? How fast will the tires be spinning from rest if the car accelerates for 1.50 minutes? And finally how fast will that be linearly?
T=90 seconds
R=.3 m

Homework Equations


Vt=rw

a=wf-wi/t

W=ø/t


The Attempt at a Solution



Homework Statement


Will a car traveling at exactly 20 mph around a corner have a tangential acceleration? Centripetal acceleration? Explain.


Homework Equations





The Attempt at a Solution

It is a poorly worded question, but it appears to be asking you to find the angular acceleration of the wheels, not the car.

AM
 
you are given dv/dt, but you need to find d\omega/dt. Use v= \omega r
 

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