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11.4 Tangent Vectors and Normal Vectors Find a unit tangent vector at a point on a space curve Find the tangential and normal components of acceleration

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Normal vector of acceleration is called the centripetal component of acceleration and is greater than or equal to 0.

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Tangential component of acceleration Rate of change of the speed Aka linear acceleration Measures the acceleration in the direction of the velocity

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Normal Vector Measures the acceleration applied at a right angle to the velocity Measures how fast the direction of the velocity vector is changing

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Find Normal and Tangential components of acceleration for

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PG. 817 # 1-9 ODD, 13, 19, 25, 54 Homework

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11.5 Arc Length and Curvature Find arc length of a space curve Arc length parameter to describe plane curves/space curves Curvature of a curve at a point on the curve Use vector-valued functions to find frictional force.

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Note: If curve is “smooth”, then ||r’(s)||=1

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Note: Since a straight line does not “curve,” its curvature is 0.

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Curvature in Rectangular Coordinates

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Acceleration, speed, and curvature pg.826 Normal component of acceleration – Function of BOTH speed and curvature – Measures acceleration acting perpendicular to direction of motion – Ex. Driving car around a turn Tangential component of acceleration=rate of change of the speed – Negative when object slows down – Positive when speeds up – Solely a function of the arc length

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Frictional Force pg. 827 A 360 kg go-cart is driven at a speed of 60 km/hr around a circular racetrack of radius 12 meters. To keep the cart from skidding off course, what frictional force must the track surface exert on the tires?

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PG. 828 # 1, 3, 7, 9 (DO NOT DRAW), 15, 17, 21-29 ODD, 37, 39, 51 Homework for Section 11.5

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