Circular motion of a train magnitude and angle

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SUMMARY

The discussion focuses on calculating the total acceleration of a train rounding a circular curve with a radius of 200 meters. The train has an angular acceleration of 1.50 X 10^-3 rad/s² and an angular speed of 0.0400 rad/s. The total acceleration is determined using the formula a_NET = √(a_c² + a_t²), where a_c is centripetal acceleration and a_t is tangential acceleration. The tangential acceleration can be calculated using the relationship between angular acceleration and tangential acceleration, specifically a_t = angular acceleration × radius.

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Homework Statement


A train is rounding a circular curve whose radius is 2.00 X 10[tex]_{}2[/tex] m. At one instant, the train has an angular acceleration of 1.50 X 10^-3 rad/s[tex]_{}2[/tex] and an angular speed of 0.0400 rad/s.
(a) Find the magnitude of the total acceleration (centripetal plus tangential) of the train.

(b) Determine the angle of the total acceleration relative to the radial direction.

Homework Equations


a[tex]_{}NET[/tex] = [tex]\sqrt{}ac2^{}_{} + at2^{}[/tex]
and Ac is the centripetal acceleration, At is the tangential acceleration


The Attempt at a Solution


i tried using this equation, but i couldn't find At. to find this, you need delta velocity divided by delta time, but there is no time and i don't know if angular speed is the same thing as regular velocity
 
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You can find At by using the formula: angular acceleration = tangential acceleration / radius.

I'm not sure how to find the angle though...
 

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