Solve Rotational Dynamics Homework: Flywheel Stopping in 3 Minutes

[Lyphta]

Homework Statement

A wheel initially rotates counterclockwise about a fixed axis, with an initial angular speed of 1.2 radians per second. If it accelerates uniformly to 2.0 radians per second clockwise during a 5 second interval, what is the magnitude of its displacement during this interval?

Homework Equations

[tex]\omega[/tex]f[tex]^{2}[/tex] - [tex]\omega[/tex]i[tex]^{2}[/tex] = 2[tex]\theta[/tex][tex]\alpha[/tex]

The Attempt at a Solution

[tex]\omega[/tex]i = 1.2 rad/sec
[tex]\omega[/tex]f = 2 rad/sec
t= 5 sec
[tex]\theta[/tex] = ?

2^2 - 1.2^2 = 2 [tex]\theta[/tex] ... But I found out I can't use that equation, that's where I've been stumped at...

Homework Statement

A flywheel initially spinning at 1800 rpm is brought to rest in 3 minutes. How many revolutions does the flywheel make in coming to rest?

Homework Equations

[tex]\omega[/tex]f[tex]^{2}[/tex] - [tex]\omega[/tex]i[tex]^{2}[/tex] = 2[tex]\theta[/tex][tex]\alpha[/tex]

The Attempt at a Solution

[tex]\omega[/tex]i = 1800 rpm
[tex]\theta[/tex] = ?
[tex]\omega[/tex]i = 0
[tex]\alpha[/tex] = -3769.9 rad/min^2
t= 3 minutes.

0 - [(1800)(2[tex]\pi[/tex]) = 2(-3769.9)([tex]\theta[/tex]
but i don't end up with 2700 rev...

 

[Shooting Star]

Homework Equations

[tex]\omega[/tex]f[tex]^{2}[/tex] - [tex]\omega[/tex]i[tex]^{2}[/tex] = 2[tex]\theta[/tex][tex]\alpha[/tex]

Do you know any other eqn apart form this? There are three major eqns for uniform acccn, whehter linear or angular. Find alpha from one of those, and then find theta.

The Attempt at a Solution

[tex]\omega[/tex]i = 1.2 rad/sec
[tex]\omega[/tex]f = 2 rad/sec

omega_f = - 2 rad/s.

Same for the other problem.

 

[Moetasim]

I would approach this problem by first converting all units to the standard SI units of radians per second and seconds. This will make the equations more straightforward to use.

First, we need to convert the initial angular speed of 1800 rpm to radians per second. We can do this by multiplying by 2π, since there are 2π radians in one revolution and 60 seconds in one minute.

So, \omegai = (1800 rpm)(2π/60 sec) = 188.5 rad/sec.

Next, we need to find the final angular speed, \omegaf, which is 0 since the flywheel comes to rest. We also know that the time, t, is 3 minutes or 180 seconds.

Now, we can use the equation \omegaf^{2} - \omegai^{2} = 2\theta\alpha to solve for the number of revolutions, \theta.

Plugging in our values, we get:

0 - (188.5)^2 = 2(θ)(-188.5/180)
-35552.25 = -2.095θ
θ = 35552.25/2.095 = 16985.5 revolutions

So, the flywheel makes approximately 16985.5 revolutions in coming to rest in 3 minutes.