Time-dependent angular acceleration problem

In summary, the problem involves a wheel with changing angular speed due to friction. The given expression for the angular speed changes from 3.96 rad/s to 3.46 rad/s in 3.92 seconds. The magnitude of the angular acceleration after 2.44 seconds cannot be determined as the constant σ is undefined in the problem and other attempted methods did not provide the correct answer."
  • #1
Ceenaya19
8
0

Homework Statement



As a result of friction, the angular speed of a
wheel changes with time according to
dθ/dt=ω0*e^-σt ,
where ω0 and σ are constants. The angular
speed changes from an initial angular speed
of 3.96 rad/s to 3.46 rad/s in 3.92 s .
Determine the magnitude of the angular
acceleration after 2.44 s.
Answer in units of rad/s2



Homework Equations


dω/dt = [tex]\alpha[/tex]


The Attempt at a Solution


I've tried differentiating the given expression for omega in an attempt to get the angular acceleration, but that didn't work because [tex]\sigma[/tex] is undefined in the problem. I've also tried taking the ln of both sides, but that didn't work either. I tried solving for [tex]\sigma[/tex] in terms of ω and ω0, but that didn't work. Finally, I tried just assuming that the acceleration is just constant from t0 to t, but that also wasn't the right answer. So, I have no idea what to try next...
 
Last edited:
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  • #2
I still can't get it O_O
 

1. What is time-dependent angular acceleration?

Time-dependent angular acceleration is a measure of the change in the angular velocity of an object over time. It is a vector quantity that describes the rate at which the object's angular velocity is changing, taking into account both its magnitude and direction.

2. How is time-dependent angular acceleration calculated?

Time-dependent angular acceleration is calculated by dividing the change in angular velocity by the change in time. This can be represented by the formula α = (ω2 - ω1) / (t2 - t1), where α is the angular acceleration, ω is the angular velocity, and t is time.

3. What is the difference between angular acceleration and linear acceleration?

Angular acceleration is a measure of the change in angular velocity, while linear acceleration is a measure of the change in linear velocity. Angular acceleration is typically measured in radians per second squared, while linear acceleration is measured in meters per second squared.

4. How does time affect angular acceleration?

Time plays a crucial role in determining the magnitude of angular acceleration. The longer the time interval, the greater the change in angular velocity and thus the greater the angular acceleration. This is because the longer the time interval, the more time the object has to change its direction and speed of rotation.

5. What are some real-world applications of time-dependent angular acceleration?

Time-dependent angular acceleration is important in understanding the motion of objects in rotational systems, such as gears, pulleys, and wheels. It is also used in sports, such as figure skating and gymnastics, to analyze the movements and rotations of athletes. In engineering, it is essential in designing machines and structures that involve rotational motion, such as turbines and bridges.

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