Video Transcript
A spinning metal disk initially has
an angular momentum of 2.4 kilograms meter squared per second. A constant torque is applied to the
disk. Over a time of four seconds, its
angular momentum increases to 3.6 kilograms meter squared per second. What is the magnitude of the torque
that is applied to the disk?
So, in this example, we have a
spinning metal disk. And we’re told that, initially,
this disk has an angular momentum — we’ll call it 𝐿 sub i — of 2.4 kilograms meter
squared per second. Then we’re told that a constant
torque is applied to the disk and that, as a result, the disk’s angular momentum
increases to this new value. This means that the torque on the
disk was in the same direction as the disk was originally spinning.
Given that all this takes place
over a time interval of four seconds — we’ll label that value Δ𝑡 — we want to solve
for the magnitude of the torque that’s applied to the disk. So then we know the disk’s initial
angular momentum, its final angular momentum — we’ve called that 𝐿 sub f. We know that this change was due to
an applied torque and that this torque was applied for a time interval of four
seconds.
And now we can recall an equation
that relates these variables, angular momentum, torque, and time, sometimes called
Newton’s second law of motion for rotation. The torque on an object is equal to
its change in angular momentum divided by a change in time. In the case of our spinning metal
disk, the magnitude of the torque applied to it is equal to its final angular
momentum minus its initial angular momentum — that difference will equal Δ𝐿 — all
divided by the change in time Δ𝑡. Since we know the values of all
three of these variables, 𝐿 sub f, 𝐿 sub i, and Δ𝑡, we can substitute them in
now.
With these values plugged in, we
can see that in our numerator, we’re subtracting 2.4 kilograms meter squared per
second from 3.6 kilograms meters squared per second. That gives us 1.2 of those units of
angular momentum. And we divide this by four seconds,
giving us a value of 0.3 kilograms meter squared per second squared or equivalently
0.3 newtons times meters. This is the magnitude of the torque
applied to the disk over this time interval.
