A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim?

Video transcript

Welcome back, everyone. We are making observations about a wheel and we are told that it has a mass of two kg with a radius of 20.5 m. We're also told that it's rotating about its central axis and it and therefore has a kinetic energy of 0.25 Jews. And we are tasked with finding what is the tangential velocity at a point on the circumference of the wheel. Well, we know to convert between angular velocity and tangential velocity, we just multiply angular velocity times the radius we have the radius. But we need to find what our angular velocity is. And here is the formula that we can use. We know that kinetic energy is equal to one half times the moment of a inertia for eight wheel times our angular velocity squared subbing in our formula for the moment of inertia. For a wheel, we have that this is one half times our mass times our radius squared times our omega squared. All right. So what does this mean? Well, we know that our kinetic energy is 0.25 and let's plug in the rest of our values, we have one half times two times 20.5 squared times our angular velocity squared. As you can see here, the one half and two just cancel out. But then I have to divide both sides by 20.5 squared. So we have 0.5 squared and that cancels out the 0.5 squared terms. On the right hand side. Finally, to get rid of the exponent on the angle velocity term, we just take the square root of both sides. You'll see that goes away. And what we get is that our angular velocity is equal to the square root of the term on the left hand side of our equation, which just works out to the square root of one which equals one. This means that our tangential velocity is equal to one times our radius of 10.5 giving us a final answer of 0.5 m per second which corresponds to answer choice. D Thank you all so much for watching. I hope this video helped. We will see you all in the next one.