Presentation on theme: "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."— Presentation transcript:
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
Normal vector of acceleration is called the centripetal component of acceleration and is greater than or equal to 0.
Tangential component of acceleration Rate of change of the speed Aka linear acceleration Measures the acceleration in the direction of the velocity
Normal Vector Measures the acceleration applied at a right angle to the velocity Measures how fast the direction of the velocity vector is changing
Find Normal and Tangential components of acceleration for
PG. 817 # 1-9 ODD, 13, 19, 25, 54 Homework
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.
Note: If curve is “smooth”, then ||r’(s)||=1
Note: Since a straight line does not “curve,” its curvature is 0.
Curvature in Rectangular Coordinates
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
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?
PG. 828 # 1, 3, 7, 9 (DO NOT DRAW), 15, 17, ODD, 37, 39, 51 Homework for Section 11.5