What Causes Discrepancies in Calculating Initial Angular Velocity?

In summary, when solving for the initial angular velocity of a wheel that rotates with a constant angular acceleration and has a given angular displacement and final velocity, it is important to include the initial angular velocity in the formula for rotational velocity. This can be done by using the third equation provided in the homework, rather than the second equation which only applies when the initial angular velocity is zero.
  • #1
AlexH
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Homework Statement


A wheel rotates with a constant angular acceleration of π rad/s^2. During a certain time interval its angular displacement is π rad. At the end of the interval its angular velocity is 2π rad/s. What is its angular velocity at the beginning of the time interval?

Homework Equations


angle displacement = (initial rotational velocity * time) + 1/2(rotational acceleration)time^2
rotational velocity = rotational acceleration * time
rotational velocity^2 = (initial rot. velocity^2) + 2(rotational acceleration)(angle displacement)

The Attempt at a Solution


When plugging in the values into the third equation, I'm able to solve the problem and get the correct answer (π*sqrt2).

But I'm wondering what's wrong with my other way of doing it.
I tried solving for the time by plugging in the final velocity and acceleration into the 2nd equation (2π = π*t), which gives t = 2.
Then I plugged the values into the first equation to try to solve for the initial angular velocity (π = (initial rotational velocity x 2) + 1/2(π)2^2
But that didn't work out. Is there a reason why?

Thanks for any help!
 
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  • #2
Your formula for the rotational velocity is not complete. You have ignored the initial rotational velocity in it.
 
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Likes AlexH
  • #3
Orodruin said:
Your formula for the rotational velocity is not complete. You have ignored the initial rotational velocity in it.
I see, thanks!
 

Related to What Causes Discrepancies in Calculating Initial Angular Velocity?

What is rotational kinematics?

Rotational kinematics is the study of the motion of objects as they rotate around a fixed axis. It involves understanding the position, velocity, and acceleration of rotating objects.

What is the difference between linear and rotational kinematics?

Linear kinematics deals with the motion of objects in a straight line, while rotational kinematics deals with the motion of objects around an axis. In linear kinematics, velocity and acceleration are measured in meters per second, while in rotational kinematics, they are measured in radians per second.

What is angular velocity and how is it calculated?

Angular velocity is the rate of change of an object's angular displacement. It is calculated by dividing the change in angular displacement by the change in time. It is measured in radians per second.

What is the difference between angular velocity and angular acceleration?

Angular velocity is the rate of change of angular displacement, while angular acceleration is the rate of change of angular velocity. Angular acceleration is responsible for changing the speed at which an object rotates.

How does rotational kinematics apply to real-life situations?

Rotational kinematics can be observed in many real-life situations, such as the motion of a spinning top, a gyroscope, or a rotating wheel. It is also important in understanding the mechanics of machines, such as engines and turbines.

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