We have a curve of radius. Uh huh. Mm. 200 m with there's an angular acceleration of 15 times 10 To the negative 3rd power radiance per second squared. Oh, erase angular acceleration. Okay. And an angular speed. 0.0 five radiance per second was the total acceleration of the train. Okay, well the centripetal acceleration is V squared over R. The tangential acceleration is oh, for our so the total acceleration, the magnitude. Hey now I still have the stuff down here. The magnitude is going to be oops square root of a c squared plus a t squared. So putting that in a calculator, square root uh, B squared over R squared. I better declare these variables. R. 200. Alfa equals £1.5. 10 To the negative 3rd B Equals went through five. So it's square it of the quantity V squared over R. And then I want to square that. Plus the quantity alpha are I don't want to square that. So that gives me 0.3 00 meters per second squared B. What's the angle relative to the radio direction? So let's say that it's here. This is the radio. No, no, no, that's not the radio direction. My bed, this is the radio direction. And so this would be tha tha so data would be the inverse tangent of the opposite over the high pot. No, opposite over adjacent. The opposite would be the tangential acceleration. The adjacent would be the centripetal acceleration. So putting that in the calculator. Okay. Of and gentle acceleration which is alpha are over V squared over our 1.570, that's in Radiance change out 2°. Uh huh. It's almost entirely in the tangential direction Gives Me 90°. Let's check Question # 47 Ha ha! I see where I made a mistake. I wrote this up here as V but it's supposed to be omega V is going to be omega are so um, down here, I need to write, well, I could write omega squared are here. Okay, let's do this again. So erase that and erase that. Okay, let's try this again. Um, so V is omega are, so that's just 10 m per second. Okay, that gives me .583 down here And then down here it gives me 30 1° and those are the correct answers.