How Do You Calculate Time in Angular Motion Problems?

[tigerlili]

Homework Statement

A flywheel turns through 22 rev as it slows from an angular speed of 6.5 rad/s to a stop. (a) Assuming a constant angular acceleration, find the time for it to come to rest. (b) What is its angular acceleration? (c) How much time is required for it to complete the first 11 of the 22 revolutions?

Homework Equations

n revolutions = 2npi radians

2npi= 1/2 alpha(t^2)
omega final^2 = omega initial^2 + 2alpha (2npi)

The Attempt at a Solution

i already got parts a and b, but i am confused about part c
the problem states that the angular acceleration is constant, so why can't i just use the kinematic analogue that i used to find the time in part a to find part c. please help!

 

[anathema]

Thank you for your question. Part c of this problem requires you to use the relation between angular displacement, angular velocity, and angular acceleration, which is given by the equation ωf^2 = ωi^2 + 2αθ, where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and θ is the angular displacement.

Since the angular acceleration is constant, you can use this equation to find the time for the first 11 revolutions by setting θ = 11 revolutions = 22π radians and solving for t. This will give you the time required for the flywheel to complete the first 11 revolutions.

I hope this helps. Let me know if you have any further questions.

 

[kerimek]

In part c, the question is asking for the time it takes for the flywheel to complete the first 11 revolutions, not just come to a stop. Therefore, you cannot simply use the same kinematic equation that you used in part a, as that only applies to the entire motion from start to finish. Instead, you need to use the equation for angular displacement, which is given by theta = theta initial + omega initial t + 1/2 alpha t^2. By setting theta equal to 11 revolutions (22*pi radians), you can solve for the time it takes for the flywheel to complete the first 11 revolutions. This will give you the answer for part c.