Angular Acceleration and wheel revolution

In summary, the wheel accelerated from rest to 59 rad/s at a rate of 29 rad/s². The equation that relates angular displacement, angular velocity, and angular acceleration is Angular Displacement = 1/2*Angular Acceleration*Time². However, since time is not given, another equation is needed to solve the problem. The initial velocity, final velocity, and acceleration can be used to calculate the time, but this requires more information.
  • #1
ecthelion4
24
0

Homework Statement



A wheel accelerates from rest to 59 rad/s at a rate of 29 rad/s². How many revolutions the wheel turned while accelerating?

Homework Equations

The Attempt at a Solution



I'm confused, I suck at this kind of problem. I got change in angular velocity which would be 59rad/s, and I got that the angular acceleration would be 29 rad/s². What equation relates all three? All equations I know relate them using time, but I got no time there.
 
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  • #2
The equation you are looking for is an EXACT analog of the equation for linear motion, s=(1/2)*a*t^2. Does that help?
 
  • #3
Not really. See that would translate into angular motion as this:

Angular Displacement = 1/2*Angular Acceleration*Time²

And since I got no time, that equation is useless. I need an equation that somehow relates ONLY angular displacement to angular velocity and angular acceleration

Unless I'm missing a way to get the time from the given data...
 
  • #4
Well, you know the initial velocity, the final velocity and the acceleration. Could that give you a time?
 
  • #5
...could it?
 
  • #6
I would say that if I accelerate from 0 to 10 m/sec at an acceleration of 10 m/sec^2, then the time it takes is 1 sec.
 

FAQ: Angular Acceleration and wheel revolution

What is angular acceleration?

Angular acceleration refers to the rate of change of angular velocity over time. In other words, it measures how quickly the rotational speed of an object is changing. It is typically measured in radians per second squared.

How is angular acceleration related to linear acceleration?

Angular acceleration and linear acceleration are related through the radius of the object's rotation. The linear acceleration of an object is equal to the angular acceleration multiplied by the radius at which the object is rotating. This relationship is described by the equation a = αr, where a is linear acceleration, α is angular acceleration, and r is the radius.

How does angular acceleration affect wheel revolution?

Angular acceleration directly affects the rotational speed of a wheel. A larger angular acceleration will result in a faster increase in the wheel's revolution, while a smaller angular acceleration will result in a slower increase. This is because angular acceleration is a measure of how quickly the rotational speed is changing.

What is the difference between angular acceleration and angular velocity?

Angular acceleration and angular velocity are both measures of rotational motion, but they are different quantities. Angular velocity measures the rotational speed of an object at a specific moment, while angular acceleration measures how quickly that velocity is changing over time. In other words, angular velocity is a measure of the rate of rotation, while angular acceleration is a measure of the rate of change of rotation.

How is angular acceleration measured?

Angular acceleration can be measured using various tools such as an accelerometer or a gyroscope. These devices can detect changes in angular velocity and calculate the corresponding angular acceleration. Additionally, angular acceleration can also be calculated using the change in angular velocity over time, as described by the equation α = (ω2 - ω1)/t, where α is angular acceleration, ω1 is the initial angular velocity, ω2 is the final angular velocity, and t is the time interval.

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