What is the angular velocity of the nail in a car tire at 55 mi/hr?

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Homework Help Overview

The problem involves calculating the angular velocity of a nail lodged in a car tire, given the car's speed of 55 miles per hour and the distance of the nail from the center of the wheel. The subject area includes concepts from rotational motion and angular velocity.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to convert the car's speed from miles per hour to inches per hour and calculates a velocity based on the radius of the tire. They question the correctness of their calculations and seek guidance on converting linear velocity to angular velocity.
  • Some participants clarify the formula for angular velocity and discuss the relationship between linear velocity, radius, and angular displacement.
  • Others raise questions about the given information, specifically the interpretation of the angle in radians and how it relates to the problem.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and clarifying the relationships between the variables involved. Some guidance has been provided regarding the use of angular displacement in the calculations, but no consensus has been reached on the correct approach yet.

Contextual Notes

Participants note the lack of explicit information regarding the time taken for one complete rotation of the wheel, which is necessary for determining angular velocity. There is also a discussion about the assumptions made regarding the angle of rotation.

Miike012
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Homework Statement


Car runs at 55 mi/hr. and the nail is lodged in tire 13 in from center of wheel, then what is the angular velocity of the nail in rad/hour?


Homework Equations



w= v/r


The Attempt at a Solution


First I will convert 55 miles into inches.
55 mile * 5280 FT/mile * 12 Inches/FT = 3484800 inches.

Velocity = 3484800 INCH/HR
R = 6.5 INCH

Thus:3484800 / 6.5 = 6969600 inch/hr
(Is this correct so far)...
then how do I convert that into rad/hr...?
Is there a formula that I am not aware of?
Please help. thank you,.
 
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The formula for angular velocity is v=r(θ/t) where r is the radius, t is time, and theta is the angle in radians, though you can use degrees if I'm not mistaken
 
But I am not given theta. Not that I am aware of anyways... I am only given 55 mi/hr and the radius.
 
actually you are given theta, it is the angle of the wheel, or 2pi radians
 
O yeah.. so do i multiply 2(pi) times 55 mi/hr / R (in miles)?
 
not quite. You know that the angle is 2pi radians you need to figure out how long it take to sweep across that distance, in other words how long does it take for the wheel to make one rotation which you can find out since you know how fast the car itself is travelling. θ/t gives you your angular speed. you then multiply by the radius to find the angular velocity.
 

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