# Trigonometeric Ratios: Tire Speed

• trigger352
In summary, The conversation is about finding the angular speed and radians traveled of a tire traveling at 100km/hr. The participants discuss using conversion factors and equations to solve the problem, but struggle with finding the correct answer and become confused. One participant eventually gives up and decides to go to bed.
trigger352
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?

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.

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

Yeah, ok. What's wrong. =P

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

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

Last edited:

## What are trigonometric ratios?

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The most common trigonometric ratios are sine, cosine, and tangent.

## How are trigonometric ratios used to calculate tire speed?

Trigonometric ratios are used to calculate tire speed by using the ratio between the tire's circumference and the number of rotations it makes per unit of time. By using trigonometric functions, we can determine the linear speed of the tire as it rotates.

## What is the importance of calculating tire speed?

Calculating tire speed is important for several reasons. It helps determine the speed of the vehicle, which is crucial for safe driving. It also plays a role in fuel efficiency and tire wear, as different speeds can affect these factors.

## How do you calculate tire speed using trigonometric ratios?

To calculate tire speed using trigonometric ratios, you need to measure the tire's circumference and the number of rotations it makes per unit of time. Then, you can use the formula speed = (circumference x rotations per unit of time) / (2 x pi) to calculate the linear speed in miles per hour.

## Are there any other applications of trigonometric ratios besides calculating tire speed?

Yes, trigonometric ratios have many other applications in various fields such as engineering, physics, and navigation. They are used to solve problems involving angles and distances, as well as in the construction of buildings and bridges.

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