Trigonometeric Ratios: Tire Speed

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Homework Help Overview

The discussion revolves around a homework problem related to trigonometric ratios and angular speed, specifically involving a car traveling at 100 km/hr and the calculations related to the angular speed of its tires with a radius of 36 cm.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the conversion of speed from km/hr to m/s and discuss the relationship between linear speed and angular speed. There are attempts to calculate the number of revolutions per second and the corresponding radians per second, with some questioning their calculations and assumptions.

Discussion Status

Multiple interpretations of the calculations are being explored, with participants providing various approaches to find the angular speed and the radians turned by the tire. Some guidance is offered regarding the relationships between distance, speed, and revolutions, but there is no explicit consensus on the correct method or final values.

Contextual Notes

Participants express uncertainty about their calculations and the conversions involved, indicating a need for clarification on the relationships between linear and angular measurements. There is a recognition of the challenge posed by the problem, which may contribute to the confusion.

trigger352
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Can someone get me started? This is a homework question that I just can't get started on.

No wonder it's a "challenge" question.

A car is traveling at 100km/hr.

A) What is the angular speed of a tire which has a radius of 36cm.

B) Through how many radians will the tire turn in 30s at this speed?
 
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100km/hr = 360m/s

In one second, it travels 360m. Think of the distance along the tire rim travelled.
Can you find how many revolutions it completes in one second? (360m).
 
whozum said:
100km/hr = 360m/s

In one second, it travels 360m.

UGH.

:rolleyes:
 
Did I butcher it?

100km/hr * 1hr/3600s * 1000m/1km = 27.77m/s

Yes I did. Sorry.
 
Wouldn't I need to divide the circumfrence by the speed?

2pi(36)=2.26m

so, 360/2.26 = 159.2920 rotations/sec. That's wrong.

Because then 2pi, for one whole rotation would be
318.5841pi/1sec = 1000.86 radians/sec


Yeah, ok. What's wrong. =P :smile:

Edit: I redit the question the same way except I substituted 27.77 for 360. I got 38.something. Which isn't right either.
 
Last edited:
27.77m/s

2.26m/rev

27.77/2.26 = xxx rev/s

Its going to be about 12-13
 
yeha, sorry - I got that much. The 38 was from the calculation to get ther radians/sec

12.2876pi/sec = 38.6027 ... Yeah I don't know what I'm doing there.
 
27.77m/s * 1rev/2.26m = 12.28rev/s
1 revolution = 2pi radians

12.28 rev = 75.4 radians

12.28rev/s = 75.4rad/sec

God now your confusing me. I'm going to bed, lol.
 
Last edited:

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