Video Transcript
A washing machine applies a torque
of 8.0 kilograms meter squared per second squared to the drum of the machine over a
period of time, giving the drum an angular impulse of 960 kilograms meter squared
per second. For how long was the torque applied
to the drum?
Alright, let’s say that this is our
washing machine drum. We’re looking down on it from
above. And so, here’s our drum full of
clothes as they’re about to be washed. And we’re told that this drum
experiences a torque, we can call it 𝜏, of 8.0 kilograms meter squared per second
squared. This constant torque is applied
over a period of time we’ll call Δ𝑡. And as a result, an angular impulse
is delivered to the drum. We’ll call this angular impulse
𝐻. And we’re told it’s equal to 960
kilograms meter squared per second. The question is, what is Δ𝑡? That is, for how long do we apply
this torque to our drum so that we got this resulting angular impulse?
To figure this out, we can recall a
mathematical relationship that connects these three variables, time, torque, and
angular impulse. The angular impulse delivered to
some object, also equal to its change in angular momentum, is equal to the torque
applied to that object times the time over which the torque is applied. For our purposes, we can shorten
this expression to read 𝐻 is equal to 𝜏 times Δ𝑡. But then, it’s not 𝐻 we want to
solve for but in our case Δ𝑡. If we divide both sides of this
equation by the torque 𝜏, we find that Δ𝑡 is equal to 𝐻 divided by 𝜏.
And now, we see how to go about
solving for Δ𝑡 in our particular scenario. It’s equal to the angular impulse
experienced by the washing machine drum divided by the torque applied to create that
impulse. Plugging in for our values of 𝐻
and 𝜏, we find that significant unit cancellation goes on. The units of kilograms and meter
squared cancel from top and bottom, as does one factor of one over seconds. This means that in the end, our
units simplify to seconds, which is good because we’re calculating an amount of
time. 960 divided by 8.0 is 120. And so, here we have our
answer. Torque was applied to this washing
machine drum for 120 seconds.
