# Constant Angular Acceleration of a wheel

• hatingphysics
In summary, at t=1.9 seconds, the wheel's angular velocity is 6.2 rad/s. However, at t=47 seconds, the angular velocity suddenly changes to 0 rad/s2.
hatingphysics
Starting from rest at t = 0 s, a wheel undergoes a constant angular acceleration. When t = 1.9 s, the angular velocity of the wheel is 6.2 rad/s. The acceleration continues until t = 15 s, when the acceleration abruptly changes to 0 rad/s2. Through what angle does the wheel rotate in the interval t = 0 s to t = 47 s?

okay...there are too many times here..what am i supposed to do for the acceleration after 25sec...to 46secs? i don't know what acceleration to to use to find the angular velocity from 25 to 46secs, to take the total velocity and find the angular displacement.

hatingphysics said:
Starting from rest at t = 0 s, a wheel undergoes a constant angular acceleration. When t = 1.9 s, the angular velocity of the wheel is 6.2 rad/s. The acceleration continues until t = 15 s, when the acceleration abruptly changes to 0 rad/s2. Through what angle does the wheel rotate in the interval t = 0 s to t = 47 s?

okay...there are too many times here..what am i supposed to do for the acceleration after 25sec...to 46secs? i don't know what acceleration to to use to find the angular velocity from 25 to 46secs, to take the total velocity and find the angular displacement.

Draw a graph, it may help. Since angular acceleration is constant, you know that angular velocity must be a linear function, whose slope you know from the first information given in the problem. The slope is enough to determine the angular acceleration.

Split this question up into two phases;

Phase One:Constant Acceleration

From t=0 to t=15, you have a constant angular acceleration, you must calculate this acceleration. You can then use this acceleration to find the angular displacement during this period.

Phase Two:Constant Angular Velocity

From t=15 to t=47 you have a constant angular velocity, which you can calculate from the above phase.

Edit: Radou beat me to it

Hootenanny said:
Edit: Radou beat me to it

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## 1. What is constant angular acceleration?

Constant angular acceleration is the rate at which an object's angular velocity changes over time, while moving in a circular motion at a constant speed. It is measured in radians per second squared (rad/s^2) or degrees per second squared (deg/s^2).

## 2. How is constant angular acceleration calculated?

Constant angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula is: α = (ωf - ωi)/t, where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time interval.

## 3. What factors affect the constant angular acceleration of a wheel?

The constant angular acceleration of a wheel can be affected by the torque applied to the wheel, the moment of inertia of the wheel, and the radius of the wheel. The greater the torque or moment of inertia, the greater the angular acceleration. The smaller the radius, the greater the angular acceleration.

## 4. How is constant angular acceleration different from linear acceleration?

Constant angular acceleration is the change in angular velocity over time, while linear acceleration is the change in linear velocity over time. In other words, angular acceleration is the measure of how fast an object's direction of motion is changing, while linear acceleration is the measure of how fast an object's speed is changing in a straight line.

## 5. How is constant angular acceleration used in real-life applications?

Constant angular acceleration is commonly used in engineering and physics to study the motion of rotating objects, such as wheels, gears, and turbines. It is also used in sports, such as figure skating and gymnastics, to describe the rotation of the body or equipment. In addition, it is used in the design of amusement park rides and roller coasters to create thrilling and safe experiences for riders.

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