A wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s^2. Compute the radial acceleration of a point on the rim for the instant the wheel completes its second revolution from the relationship (b) a_rad = v^2/r

Video transcript

Welcome back, everybody. We are making observations about a parked vehicle that drives off. We're told a couple of different things. We're told that when looking at the tires, the tires have a uniform angular acceleration of eight radiant per second squared. You're told that each tire also has a radius of 20.5 cm or .205 m. And we are tasked with finding what is the radial acceleration After a total of four revolutions have been completed. Let's take a look at our answer choices here. We have a 13.1 m per second squared. B eight m per second squared C 20.1 m per second squared or D 82.8 m per second squared. What we are told what formula we need to use here, we know that radial acceleration is equal to tangential velocity divided by the radius. Well, what is going to be tangential velocity, tangential velocity is given by the radius times whatever angular velocity we're interested in. In this case, it's after a certain number of revolutions. So we're gonna be kind of looking for that final angular velocity there. Keeping in mind it was a parked vehicle. So we started out at zero radiance per second. Now, here's what I'm gonna do. I'm gonna move this over here and I'm actually going to sub in the value for velocity into this equation right here. And so what we can get from that, we see that radial acceleration is equal to R squared times our final velocity squared, all divided by R which just gives us that our radial acceleration is equal to our radius times our final angular velocity squared. But we need to find this final angular velocity. And how are we going to do that? Well, we can use a kinematic formula that states that our final angular velocity is equal to the square roots of our initial angular velocity squared plus two times our angular acceleration times the total angular displacement Before plugging things into this formula. However, we need to make sure everything is in the correct units, our angular acceleration and our initial angular velocity is but our angular displacement is not. We need it in radiance. We know in one revolution there is two pi radiant. So what this gives us is eight pi radiant. Great. So now let's go ahead and plug everything into here. We have that our final angular velocity is equal to zero squared plus two times eight times eight pi let me extend out the radical a little bit and this gives us 20. radiance per second. Wonderful. Now that we have that. We are ready to go ahead and find our radial acceleration. We have that our radial acceleration is equal to our radius of 0.2 oh five times 20.1 squared. Giving us a final answer of 82. m per second squared corresponding to our final answer. Choice of D Thank you all so much for watching. I hope this video helped. We will see you all in the next one.