Find Speed & Acceleration of Stone in a Rotating Tire

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SUMMARY

The discussion focuses on calculating the speed and acceleration of a stone lodged in the tread of a rotating tire with a radius of 0.319 m, rotating at 98.4 revolutions per minute (rev/min). The correct tangential speed of the tire is determined using the formula V=2*pi*r*f, resulting in a speed of 197.22 m/s. However, participants emphasize the importance of converting the rotational speed from rev/min to seconds for accurate calculations. The acceleration is derived using the formula ac= v²/r.

PREREQUISITES
  • Understanding of rotational motion and tangential speed
  • Familiarity with the formulas V=2*pi*r*f and ac= v²/r
  • Basic knowledge of unit conversions, particularly from revolutions per minute to seconds
  • Concept of centripetal acceleration
NEXT STEPS
  • Learn about unit conversion techniques for rotational motion
  • Study the concept of centripetal acceleration in detail
  • Explore examples of tangential speed calculations in different contexts
  • Investigate the effects of varying tire radius on speed and acceleration
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics and kinematics, as well as educators looking for practical examples to illustrate these concepts.

Muneerah
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Homework Statement


A tire 0.319 m in radius rotates at a constant
rate of 98.4 rev/min.
Find the speed (relative to the tire’s axle)
of a small stone lodged in the tread on the
outer edge of the tire.
Answer in units of m/s.

Find the acceleration of the stone.
Answer in units of m/s2.


Homework Equations



V=2*pi*r*f
ac= v2/r

The Attempt at a Solution


I basically solved for the velocity of the tire which is 197.22 m/s
how do you find the relative speed ?? If you could find the velocity I would be able to solve for the acceleration. Thank you
 
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Muneerah said:

Homework Statement


A tire 0.319 m in radius rotates at a constant
rate of 98.4 rev/min.
Find the speed (relative to the tire’s axle)
of a small stone lodged in the tread on the
outer edge of the tire.
Answer in units of m/s.

Find the acceleration of the stone.
Answer in units of m/s2.


Homework Equations



V=2*pi*r*f
ac= v2/r

The Attempt at a Solution


I basically solved for the velocity of the tire which is 197.22 m/s
how do you find the relative speed ?? If you could find the velocity I would be able to solve for the acceleration. Thank you
You are calculating the tangential speed of a point on the outer surface of the tire. How does that compare to the speed of the stone?

Check your units. Your answer is not correct. (You are given the rotational speed in revolutions per minute, not seconds).

AM
 

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