# Solving Angular Rotation w/ Constant Acceleration - Emilie

• ~angel~
In summary, The problem at hand involves a rotating wheel with a constant angular acceleration of 2.25 rad/s^2. After 4 seconds, the wheel has rotated 60.0 rad. The question asks for the initial angular velocity of the wheel at the beginning of the 4.00 second interval. The correct approach is to use the formula \bar{\omega}=\frac{\omega_2+\omega_1}{2}=\frac{\Delta \theta}{\Delta t}. Using the given information, the answer is 3.75 rad/s. The incorrect approach of using a = (w2-w1)/ (t2-t1)
~angel~
I've been trying to do this question in the textbook, but I can't seem to get the answer.

Emilie's potter's whel rotates with a constant 2.25 rad/s^2 angular acceleration. After 4 seconds the wheel has rotated through an angle of 60.0 rad. What was hte angular velocty of the wheel at the beginning of the 4.00 second interval.

I thought I could use a = (w2-w1)/ (t2-t1), but I end up with 6 as my answer, which is incorrect.

Ok, I've got it. But why is my method incorrect?

~angel~ said:
Ok, I've got it. But why is my method incorrect?

Because:

$$\omega_2\ne\frac{\Delta \theta}{\Delta t}=15\ rad/s$$

Actually,

$$\bar{\omega}=\frac{\omega_2+\omega_1}{2}=\frac{\Delta \theta}{\Delta t}$$

## 1. How is angular rotation defined?

Angular rotation is a measure of the change in angle of an object over time. It is typically measured in radians per second.

## 2. What is constant acceleration in relation to angular rotation?

Constant acceleration refers to a situation where the angular velocity of an object changes at a constant rate over time. This results in a linear relationship between the angular velocity and time.

## 3. How do you solve for angular rotation with constant acceleration?

To solve for angular rotation with constant acceleration, you can use the formula θ = θ0 + ω0t + 1/2 αt2, where θ is the final angular position, θ0 is the initial angular position, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time.

## 4. What are some real-life examples of angular rotation with constant acceleration?

Examples of angular rotation with constant acceleration include the motion of a spinning top, the rotation of a carousel, and the movement of a satellite orbiting the Earth.

## 5. How can understanding angular rotation with constant acceleration be useful in the field of science?

Understanding angular rotation with constant acceleration is crucial in various areas of science, such as physics, engineering, and astronomy. It allows us to predict and analyze the movement of objects in rotational motion, which is essential in designing and optimizing machines and structures.

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