Lecture5-2A

Lecture5-2A - Circular Motion and Acceleration Consider the...

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Circular Motion and Acceleration Circular Motion and Acceleration Consider the two unit vectors that are convenient for angular motion: r cos i sin j sin i cos j The position vector can now be written r r r r cos i sin j x i y j The velocity vector is simply the time derivative of the position vector. For circular motion the radius of curvature, r , is constant. However, is time dependent. This means to find the velocity vector we must be careful when taking the derivative of the position vector – chain rule! t
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Circular Motion and Acceleration Consider the two unit vectors that are convenient for angular motion: r cos i sin j sin i cos j The velocity vector can now be expressed: Taking the derivative of the velocity yields the acceleration. Assuming a constant rate of rotation, w : The radial acceleration points radially inward ! What happens when there is angular acceleration? Stay tuned! v d r dt r d cos dt i d sin dt j v r sin i cos j d dt r v a d v dt r d sin dt i d cos dt j
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Lecture5-2A - Circular Motion and Acceleration Consider the...

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