# Find the average angular acceleration of the sprinter

• x2017
In summary, the sprinter ran a 200 m race in 11.61 s, with the first part of the race in a lane with a radius of 32.4 m. At 3.59 s, his speed was 5.9 m/s and at 7.9 s, his speed was 8.4 m/s. His speed after the curve was 12.4 m/s. To find his average angular acceleration after 11.61 s, the change in angular velocity divided by the change in time must be calculated. Using the equation α=Δω/Δt, the average angular acceleration is 1.34 degrees/s2. However, this answer is incorrect as it only
x2017

## Homework Statement

A sprinter runs the curve of this 200 m in 11.61 s. Assume he ran in a lane which makes a semicircle (r = 32.4 m) for the first part of the race. At 3.59 s into the race his speed is 5.9 m/s. At 7.9 s into the race his speed is 8.4 m/s. His speed after the curve was 12.4 m/s.

What was the sprinter's average angular acceleration after 11.61 s? Answer in deg/s2. I.e., what was his average acceleration while running the curve?

α=Δω/Δt

ω=Δθ/Δt

## The Attempt at a Solution

ω=Δθ/Δt
ω=180/11.61s
ω=15.50degrees/s

α=Δω/Δt
α=15.50degrees/11.61s
α=1.34degrees/s2My answer is wrong and no matter what I do I can't get it right. The way my professor does assignments is we either get 100% or 0% and so I'm very frustrated and would really really appreciate some help. Physics is very difficult for me.

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The ##\omega## you calculated is the average angular speed. You want the change in angular speed from start to end of curve.

The average acceleration is the change in velocity divided by the change in time for the interval in question. That's your first relevant equation. In this case you're dealing with angular measures, so the average angular acceleration would be the change in angular velocity divided by the change in time.

Your second relevant equation determines the average velocity. But that's not what you're looking for.

The problem statement gives you the sprinter's linear speed at various points along the curve. What is the relationship between the linear (or in this case tangential) speed and the angular speed at a given time? What are the angular speeds at the beginning and end of the curve?

edit: Oops! haruspex got in there before me

## 1. What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It measures how quickly an object's rotational speed is changing.

## 2. How is angular acceleration different from linear acceleration?

Angular acceleration measures the change in rotational speed, while linear acceleration measures the change in linear speed. They are both measures of how quickly an object's velocity is changing, but in different directions.

## 3. How do you calculate the average angular acceleration of a sprinter?

To calculate the average angular acceleration of a sprinter, you need to know the initial and final angular velocities, as well as the time it takes for the sprinter to go from the initial to the final velocity. The formula for average angular acceleration is: average angular acceleration = (final angular velocity - initial angular velocity) / time.

## 4. Why is average angular acceleration important for sprinters?

Average angular acceleration is important for sprinters because it can help determine how quickly they are able to change their rotational speed during a sprint. This can be useful for improving performance and identifying areas for improvement.

## 5. How can average angular acceleration be measured for a sprinter?

Average angular acceleration can be measured using instruments such as an accelerometer or a gyroscope, which can track changes in rotational speed over time. These measurements can then be used to calculate the average angular acceleration of the sprinter.

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