this problem you given the mass you given the radius and you also given the angular velocity and the total angle that you need to find out what is the torque acting on to the system let me explain this one so you have a uniform sphere so this is a sphere and this is fear for example earth is spinning about Y axis here this is reading about its stature so it is spinning about its axis and then it is shell angular velocity is given so let's write down all the [Music] the mass is given which is 1.85 the diameter the diameter is given which is 45 centimeter in order diameter you can calculate the radius was the D over to 25 over 2 is 22 point 5 centimeter you need to change the center with to the emitter so if you do that you'll get to the point 2 5 meter this is it meter new and then it's also saying the angular velocity and velocity is denoted by Omega is given to point 4 revolution this is the evolution first second so if you see if something is rotating in one complete revolution the total angle it affects is 2 pi okay if something is rotating if you rotate one time complete then the total angle it moves is a power is exactly 2 pi so you need to check its way into into the Radian so what the way we do it you just multiply this one by 2 pi because in one complete revolution the total angle is two pi Radian okay so just plug in all the numbers yet and they you'll get is fifteen point one second okay do given T and the total angle the total angle is given is 18.2 revolution here that evolution is the angle okay it's eighteen point so in the one revolution again what's that anger total angle which is two pi so if it has completed 18 point two revolution the total angle is okay one one four point three ready and now he was an equation to solve this problem [Music] we know that in linear motion while USBs but remember in translational motion but in now we're talking about the rotational dynamics for rotational motion instead of using the V we have Omega s squared this is the final this is omega naught as well initial angular velocity to is a constant and this is a linear acceleration and in rotational dynamics we use alpha as an exploration this is the distance then protestor Donna makes the distance in angle how returns it has moved so this is the theta so this is the formula we're going to use it and it says after 1822 devolution it comes to a stop okay so the final velocity is 2 and Omega naught is given here another scholly this is any substance is putting away they are not meant that arrow because general presumption initial so this is fifteen point one point one you can put the negative sign or he's just soft for it and you'll get alpha as a negative it doesn't matter it just gives you the acceleration or what I call D exploration okay I'm just putting the positive side and you should be getting alpha as a negative need to have an Alpha and the theta is eight point one hundred fourteen point three close to one Radian per second square Isabel you get what are the negative in here the negative simply means the angular velocity is slowing down okay that's what the negative means here and we give it a sphere what is the moment of inertia of a sphere the moment of inertia is same as the mass in distant animation if you have a sphere a solid sphere this is equal to 5 over 5 the mass is given which 1.85 the radius is given to the radius so what's a plug in the this number the answer he will get it zero point in the moment of inertia will get it zero point zero three seven meter is the moment of inertia he'll get it and now the last thing is finding the talking but our is I times I love that this the same as using F is equal to M a linear motion you have F but it translational moves in a problem and Lydia mostly have mass and in rotational motion you have I and this is the linear expression you have a situation so like all the numbers here what is the torque what is the moment of inertia of Pancho Fisher alpha alpha already have calculator which is close to negative one you don't need to put the negative this is zero point zero the magnitude is simply equal to 0.03 so the negative sign simply tells you the force is dropping down or slowing down the angular velocity it is coming to rest a certain point that's what it means okay