Linear Kinematics
Uniaxial motion is one in which the motion occurs only in one direction, and it is the simplest form of linear or translational motion. A car traveling on a straight highway, an elevator going up and down in a shaft, and a sprinter running a 100-m race ar
- PDF / 464,574 Bytes
- 30 Pages / 595.276 x 790.866 pts Page_size
- 33 Downloads / 235 Views
Linear Kinematics
7.1 Uniaxial Motion / 151 7.2 Position, Displacement, Velocity, and Acceleration / 151 7.3 Dimensions and Units / 153 7.4 Measured and Derived Quantities / 154 7.5 Uniaxial Motion with Constant Acceleration / 155 7.6 Examples of Uniaxial Motion / 157 7.7 Biaxial Motion / 163 7.8 Position, Velocity, and Acceleration Vectors / 163 7.9 Biaxial Motion with Constant Acceleration / 166 7.10 Projectile Motion / 167 7.11 Applications to Athletics / 170 7.12 Exercise Problems / 175
# Springer International Publishing Switzerland 2017 ¨ zkaya et al., Fundamentals of Biomechanics, DOI 10.1007/978-3-319-44738-4_7 N. O
149
Linear Kinematics
151
7.1 Uniaxial Motion Uniaxial motion is one in which the motion occurs only in one direction, and it is the simplest form of linear or translational motion. A car traveling on a straight highway, an elevator going up and down in a shaft, and a sprinter running a 100-m race are examples of uniaxial motion. Kinematic analyses utilize the relationships between the position, velocity, and acceleration vectors. For uniaxial motion analyses, it is usually more practical to define a direction, such as x, to coincide with the direction of motion, define kinematic parameters in that direction, and carry out the analyses as if displacement, velocity, and acceleration are scalar quantities.
7.2 Position, Displacement, Velocity, and Acceleration Consider the car illustrated in Fig. 7.1. Assume that the car is initially stationary and located at 0. At time t0, the car starts moving to the right on a straight horizontal path. At some time t1, the car is observed to be at 1 and at a later time t2 it is located at 2. 0, 1, and 2 represent positions of the car at different times, and 0 also represents the initial position of the car. It is a common practice to start measuring time beginning with the instant when the motion starts, in which case t0 ¼ 0. The position of the car at different times must be measured with respect to a point in space. Let x be a measure of horizontal distances relative to the initial position of the car. If x0 represents the initial position of the car, then x1 ¼ 0. If 1 and 2 are located at x1 and x2 distances away from 0, then x1 and x2 define the relative positions of the object at times t1 and t2, respectively. Since the relative position of the car is changing with time, x is a function of time t, or x ¼ f ðtÞ. In the time interval between t1 and t2, the position of the car changed by an amount Δx ¼ x2 x1 , where Δ (capital delta) implies change. This change in position is the displacement of the car in the time interval Δt ¼ t2 t1 . During a uniaxial horizontal motion, the car may be located on the right or the left of the origin 0 of the x axis. Assuming that the positive x axis is toward the right, the position of the car is positive if it is located on the right of 0 and negative if it is on the left of 0. Similarly, the displacement of the car is positive if it is moving toward the right, and it is negative if the car is moving toward the
Data Loading...
