# How Does Uniform Angular Acceleration Affect Wheel Rotation Over Time?

In summary, the conversation discusses a wheel undergoing uniform angular acceleration with an initial angular velocity of zero. The first 1-s time interval shows the wheel rotating through an angle of 88.3 degrees, with the second 1-s time interval resulting in a rotation of 264.64 degrees. The individual is unable to determine the angle for the third 1-s time interval, but has found the angular acceleration to be 1.54 using the equation for angular acceleration. They then use this value to calculate the final angle for the second time interval. However, they are unsure of how to manipulate the angular acceleration for the third interval and ask for assistance.

A wheel is subjected to uniform angular acceleration. Initially its angular velocity is zero. During the first 1-s time interval, it rotates through an angle of 88.3

Through what angle does it rotate during the next 1-s time interval? - I found the second 1-s time interval to rotate through an angle of 264.64 deg.

Through what angle during the third 1-s time interval? - I can't seem to figure the angle for this time interval

Ok So for the first part I found the angular acceleration to be 1.54 from the equation angular acceleration= (wf - wi)/change in time for the first angle change 88.3. I used this angular acceleration in the eqn. Change of Angle = Wi (change time) + 1/2(angular acceleration)(change time)^2 I plugged in 2 for the change in time here. I took that answer which was 352.94-88.3 to get final angle of 264.64. I don't know how to manipulate the angular acceleration for the third 1-s interval, but i believe for this one i plug in 3 for the time change... then subtract the angles from the first two intervals to get the final interval.

Last edited:
Why don't you try telling us what you've done so far and how you've done it? You'll get more help if you do that.

Great job on solving the first part! To find the angle for the third 1-s interval, you can use the same equation: Change of Angle = Wi (change time) + 1/2(angular acceleration)(change time)^2. But this time, you can plug in 3 for the change in time and the same angular acceleration of 1.54. Then, you can subtract the angles from the first two intervals (264.64 deg and 88.3 deg) to get the final angle for the third interval. So it would be 352.94 deg - (264.64 deg + 88.3 deg) = 0 deg. This means that the wheel did not rotate during the third interval, which makes sense since it reached its maximum velocity during the second interval and maintained that velocity for the third interval. I hope this helps!

## What is Uniform Angular Acceleration?

Uniform Angular Acceleration is a measure of how quickly an object's angular velocity changes over time. It is a constant rate of change in the object's rotational speed.

## How is Uniform Angular Acceleration calculated?

Uniform Angular Acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula for uniform angular acceleration is: α = (ω2 - ω1) / (t2 - t1), where α is the angular acceleration, ω2 and ω1 are the final and initial angular velocities, and t2 and t1 are the final and initial times.

## What is the unit of measurement for Uniform Angular Acceleration?

The unit of measurement for Uniform Angular Acceleration is radians per second squared (rad/s²). This unit represents the amount of change in angular velocity (in radians per second) over a given time interval (in seconds).

## What is the difference between Uniform Angular Acceleration and Non-Uniform Angular Acceleration?

Uniform Angular Acceleration occurs when an object's angular velocity changes at a constant rate. This means that the object's rotational speed increases or decreases by the same amount at regular intervals. Non-Uniform Angular Acceleration, on the other hand, occurs when the rate of change in angular velocity is not constant, meaning the object's rotational speed changes at irregular intervals.

## What are some real-world examples of Uniform Angular Acceleration?

Some real-world examples of Uniform Angular Acceleration include a spinning top, a rotating ceiling fan, a bicycle wheel in motion, and a spinning figure skater. In all of these examples, the objects experience a constant rate of change in angular velocity, resulting in uniform angular acceleration.

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