Question Video: Calculating Torque Using Angular Impulse

A washing machine applies a torque of 8.0 kg.m²/s² to the drum of the machine over a period of time, giving the drum an angular impulse of 960 kg.m²/s. For how long was the torque applied to the drum?

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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.

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