 Let's solve a question on angular impulse. Here we have a boat's propeller which has a rotational inertia of 3 kgm2. After a constant torque is applied for 10 seconds, the propeller's angular speed changes from a clockwise of 5 radians per second to a counterclockwise 5 radians per second. What was the torque applied to the propeller? And we need to answer using a coordinate system where the counterclockwise direction is positive. As always pause the video and first try this one on your own. Alright, hopefully you have given this a shot. Now there is a lot of information in this question. And what I usually do is I try to list down everything that I know and then I move on to the relations and the formulas. So first I'll try to list down everything that we know, all the information that there is in this question. So we have rotational inertia which is 3 kgm2, so this is i, i is 3 kgm2. And then we have a constant torque which is applied for 10 seconds. So there is an initial angular speed which is clockwise of 5 radians per second. So I will write omega i, omega i is minus 5 radians per second. I'm writing minus because we need to assume the counterclockwise direction is positive. And initially the angular speed is in the clockwise direction, so this is minus 5. And the torque is applied for 10 seconds, so we have delta t which is 10 seconds. So now the final speed becomes, the final angular speed this becomes plus, plus 5 radians per second, plus because now it is in counterclockwise direction. And we need to figure out the torque, so tau, we don't know this, we need to figure out tau. Okay, so this is all that we know and we also know that angular momentum, angular momentum is changed when there is a torque applied over a certain interval of time. So delta L, we know that delta L change in angular momentum, this is torque into a certain time interval delta t. Just like how linear momentum is changed when a force is applied over a time interval, angular momentum is changed when a torque is applied over a time interval. So this delta L we can expand this, we can write this as final angular momentum minus initial and this is equal to tau into delta t. Now we need to figure out what tau is, what torque is. So let's write everything, so let's take everything on one side and keep this variable of torque on one side. So that will be tau, this is equal to Lf minus Li divided by delta t. Okay, now we know what delta t is and we don't yet know what the final and the initial angular momentum is. But we do know that angular momentum, this is equal to rotational inertia multiplied by the angular velocity, this is given by this relation right here. So we can write Lf, Lf is just i into omega f, Lf is just i into omega f and let's do that. So this Lf in place of Lf, we can write i into omega f and in place of Li, in place of Li, we can write i into omega i, that is the initial angular velocity. So now we can work this out, we can take i as common, when we take i as common, this becomes omega f minus omega i. So let me let me do that, this is, this will be i into omega f minus omega i. And i is 3, so let's write 3, this is 3 into omega f is plus 5, plus 5 minus omega i which is minus 5. So this becomes minus of minus 5, that will be plus 5, so this becomes 5 plus 5 divided by, divided by delta t which is, which is 10. So 5 plus 5 is 10, 10 into 3 is 30 and 30 divided by 10, this comes out to be equal to 3 Newton meters. So that is the talk applied over a period of 10 seconds to change a board's propeller angular speed from minus 5 to plus 5.