# Angular Velocity: Find Initial Velocity Given Acceleration & Displacement

• blaze33
In summary, the problem involves a wheel rotating with a constant angular acceleration of pie rad/s^2. The angular displacement during a certain time interval is pie rad and the final angular velocity is 2pie rad/s. The task is to find the initial angular velocity, but the time interval is unknown. The key is to use the equation w^2 = Wo^2 + 2(alpha)(deltatheta), which involves the initial and final velocities, angular acceleration, and angular displacement.
blaze33

## Homework Statement

a wheel rotates with a constant angular acceleration pie rad/s^2. during a certain time interval its angular displacement is pie rad. at the end of the interval its angular velocity is 2pie rad/s. what is the angular velocity at the beginning of the interval?

## Homework Equations

tried looking at the angular velocity/displacement/acceleraions equations but i don't know how to even begin this question.

## The Attempt at a Solution

well i have to find the initial angular velocity and the time interval is also unknown.

In the problem angular acceleration, angular displacement and final velocity is given. Can you find an equation which contain initial velocity, final velocity, angular acceleration and angular displacement.

yes but it also has time, which is uknown.

Lol at U of M exam questions ;). This one's simple, the key is constant acceleration.

w^2 = Wo^2 +2(alpha)(deltatheta) should do the trick ;)

lol jegues thanks.
hope the exam will be simpler than that haha

## 1. What is angular velocity?

Angular velocity is a measure of the rate at which an object rotates around a fixed point. It is usually measured in radians per second or degrees per second.

## 2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angle by the change in time. It can also be calculated by multiplying the angular speed (in radians per second) by the radius of the circle.

## 3. What is the relationship between angular velocity, acceleration, and displacement?

Angular velocity is directly proportional to acceleration and displacement. This means that as angular velocity increases, so does acceleration and displacement also increases. Similarly, a decrease in angular velocity leads to a decrease in acceleration and displacement.

## 4. Can angular velocity be negative?

Yes, angular velocity can be negative. A negative angular velocity indicates that the object is rotating in the opposite direction compared to a positive angular velocity.

## 5. How can I find the initial velocity given acceleration and displacement?

To find the initial velocity, you can use the formula v0 = √(v^2 - 2ad), where v is the final velocity, a is the acceleration, and d is the displacement. Alternatively, you can also use the formula v0 = v - at, where t is the time taken to reach the final velocity.

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