00:01
So, you have a wheel of radius r equals 0 .5 meters rolling on a smooth horizontal surface.
00:08
The wheel is initially rotating at a frequency of one revolution per second.
00:13
And then, okay, there's some weird typos going on here.
00:16
At t equals zero, the wheel slows down with an angular acceleration of alpha equals minus 0 .2 t squared.
00:24
The time t is in seconds and alpha is in radiance per second squared.
00:29
What makes this is a bit suspicious is that if you're rolling on a smooth horizontal surface, the only thing that's really affecting it is, i guess, friction.
00:41
And friction is a force that's constantly, especially if it's rolling friction, it should only be applying a constant force.
00:49
And constant force means constant acceleration.
00:52
If your alpha is dependent on t, then it's not constant.
00:58
And particularly here, as time goes on, the acceleration increases.
01:04
So it's like some weird forces being applied on this wheel somehow.
01:08
So unless we're living in a different universe with different physics, i doubt this is the case.
01:14
But more than that later.
01:15
In any case, part a is just simply asking for the frequency of revolution in hertz.
01:21
Hertz is basically revolution or a full rotation per second.
01:25
And so it's actually just straight up given to us.
01:29
It says initially rotating at frequency of one revolution per second.
01:34
So frequency is 1 hertz.
01:37
Similarly, for part b, determine the initial angular velocity at t equals zero of the wheel in regions per second.
01:45
Well, it's telling us that it's initially at one revolutions per second, and at a revolution, it's basically 2 pi radiance.
01:54
That's the entire that's 2 pi radiance is the angle for a full revolution so that gives us omega 0 equals 2 pi radiance per second part c is get is where it gets ify uh so another reason why i was actually thinking it's a typo is because it says at t equals zero so why would you say at t equals zero and give us a formula that's dependent on t if it was at t equals zero then you could just plug in t equals zero here maybe it's a t greater and zero.
02:25
I don't know what the typo is.
02:28
I'm going to assume it's a typo, but i did split c into two cases.
02:32
So if it's a typo, then we really just have a constant acceleration of negative 0 .2.
02:38
And either you memorize this if you're in a physics class or you do differential calculus.
02:44
If you do calculus, you just integrate this to get the velocity dependent on time.
02:52
So if your alpha is negative 0 .2, then you degrade it to get alpha t plus a constant, which is the concept being omega -0, omega -0 being 2 -py here.
03:03
So omega -t equals 2 -pi minus 0 .2 t.
03:06
It's just got clean and simple.
03:09
If it was not somehow a typo, then alpha is given by negative 0 .2t squared.
03:15
And if you integrate that, you get omega -t -t equals the initial, which is omega -0, minus 0 .2 over 3 t -c cubed...