Video Transcript
A torque of 0.2 kilograms meter
squared per second squared is applied to an object for 20 seconds. Then, a torque of 0.5 kilograms
meter squared per second squared is applied to the object for five seconds. What is the total angular impulse
given to the object? Give your answer to two significant
figures.
Okay, in this example, we have
torques acting on an object. And we may as well say that this
here is our object. We can imagine, say, that it’s a
disc capable of spinning around its center. What happens first is we apply a
torque, we can call it 𝜏 one, to this object. And that’s the torque given as 0.2
kilograms meter square per second. And this torque is applied for an
amount of time we can call 𝑡 one, which is 20 seconds. Then, after all this, a second
torque, we can call it 𝜏 two, is applied to our object. This is the torque of 0.5 kilograms
meter squared per second squared. This second torque is applied for a
period of time we can call 𝑡 two, which is given as five seconds. Knowing all this, we want to
calculate the total angular impulse given to the object.
Now, at this point, we can recall
that angular impulse, typically symbolized with a capital 𝐻, is equal to a change
in angular momentum. And using a rotational form of
Newton’s second law of motion, we can say that Δ𝐿, the change in angular momentum
and therefore the angular impulse, is equal to the torque applied to an object
multiplied by the time period over which that torque is applied. All this means that to calculate
the total angular impulse delivered to our object, we’ll call that 𝐻, what we’ll
want to do is add together these two torques multiplied by the times over which the
individual torques act.
Torque one, we saw, acts for a time
𝑡 one, and torque two acts for a different time 𝑡 two. Now, each one of these products by
itself is an amount of angular impulse. But to calculate the total, we’ll
need to add them. So, what we do then is substitute
in the values for 𝜏 one, 𝑡 one, 𝜏 two, and 𝑡 two. Note that in both cases, we have
units of kilograms meter squared per second squared multiplied by units of
seconds. And so, in both terms, one factor
of seconds cancels out. This means the two separate angular
impulses applied to our object are 0.2 times 20 kilograms meter squared per second
and 0.5 times five kilograms meter squared per second.
0.2 times 20 is four. And 0.5 times five is 2.5. So, to two significant figures, our
answer is 6.5 kilograms meter squared per second. This is the total angular impulse
given to the object.
