 Let's solve a question on torque and angular acceleration. Here we have a mass which is attached to a chord that is wrapped around a pulley. The pulley has a moment of inertia of 0.05 kilogram meter square and is free to rotate about an axis through its center. Now at time t equals to zero the mass is released and allowed to fall rotating the pulley and the resulting torque on the pulley is 1.40 Newton meters. We need to figure out the angular velocity of the pulley after 0.5 seconds. All right so now for this one let's try and draw what the what the situation is. Here we have we have a pulley and let me make it over here. Here we have the pulley and we also have a mass so let's make that as well. The mass is let's say here is the mass and there's there's a string there's a string through which there's a chord through which the mass is connected to the pulley. So let's say here here it is this is this is a chord. All right so now there is some information that we already know which is which is that the moment of inertia of this pulley that is 0.05 kilogram meter square. So let's let's write that this is 0.05 kilogram meter square and let's say this instant is t equals to zero this instant right here is t equals to zero this mass starts falling and when it falls there is a torque because of the tension force in this string. There's a torque which is zero point sorry not zero point this is 1.40 Newton meters. As a result of this torque this pulley starts rotating this pulley starts rotating and and we can say that it starts rotating with an angular acceleration of alpha because there is a torque so there will be an angular acceleration. Using the rotational version of Newton's second law we can write we can write tau this is equal to i alpha this is the rotational version of Newton's second law right. So we know torque and here we know the moment of inertia we can figure out the angular acceleration and once we figure out the angular acceleration we can go to one rotational kinematic equation and then use one to figure out the final angular velocity the final angular velocity. Initial angular velocity is already zero and we already know the time so if we figure out alpha our job is done okay now first let's figure out what alpha is we know tau we know tau that is this is what is this this is 1.4 so 1.4 equals 0.05 into alpha so alpha this is 1.4 divided by 0.05 this is 28 28 radians per second square now we know alpha we know omega i and we know time so we are not interested in figuring out the angular displacement so the right kinematic equation the right rotational kinematic equation can be this one the final angular velocity which is equal to the initial angular velocity plus alpha into t so initial angular velocity is zero and alpha is 28 and t is 0.5 so omega f this comes out to be equal to 28 into 0.5 which is 14 radians per second so this right here this is 14 radians per second now you can try more questions like this from the exercise in the lesson and if you're watching on youtube do check out the exercise link which is added in the description.