Circular motion of a train magnitude and angle

AI Thread Summary
The discussion focuses on calculating the total acceleration of a train rounding a circular curve with a radius of 200 meters, given its angular acceleration of 1.50 x 10^-3 rad/s² and angular speed of 0.0400 rad/s. The total acceleration is determined using the formula for net acceleration, which combines centripetal and tangential components. To find the tangential acceleration, the relationship between angular acceleration and tangential acceleration is utilized, with the formula linking them through the radius. The challenge remains in calculating the angle of the total acceleration relative to the radial direction. Overall, the problem emphasizes the need to clarify the relationship between angular and linear velocities in circular motion.
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Homework Statement


A train is rounding a circular curve whose radius is 2.00 X 10_{}2 m. At one instant, the train has an angular acceleration of 1.50 X 10^-3 rad/s_{}2 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_{}NET = \sqrt{}ac2^{}_{} + at2^{}
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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