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Lecture 20

# Lecture 20 - Lecture 20 pls-20.1 Rotational Kinematics II...

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Lecture 20 pls-20.1 Rotational Kinematics II Media: 1. Solid disc Clicker questions 1 – 3 . 1. Tangential Variables Consider an object rotating with angular velocity dt d θ ω = and angular acceleration dt d ω α = . Now consider a particular point on the object, as illustrated in either picture above. Because the point moves in a circle, its velocity is tangent to the circle. The magnitude of velocity of the point is related to the angular velocity ω via ω r v T = where here all variables are magnitudes. The T subscript is not really necessary, but it reminds us that the velocity is tangential to the circle that describes the motion. Let’s consider the time derivative of this equation, dt d r dt dv T ω = . 1 s 1 r . 2 s 2 r θ θ T v T v

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Lecture 20 pls-20.2 Now α ω = dt d and we identify T T a dt dv as the tangential component of the acceleration, and so we have α r a T = 2. Centripetal and Tangential Acceleration (Components) Because the point is moving in a circle it also has, at any point in time, a centripetal component of acceleration (as we discussed in the context
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