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KIN3323 Biomechanics Exam #2 Study guide Linear kinematics At the completion of this unit, students should be able to: List and describe the 3 types of motion.
**1. Rectilinear Motion: Movement along a straight-line path
- Curvilinear Motion: Movement along a curved path
- Angular Motion: All points on an object move in circles about the axis.** Describe how the cartesian coordinate system is used to describe the position. o Position: Location of a point within a reference frame o Cartesian coordinate system: Fixed origin with axes that are perpendicular to each other. 2D or 3D.
o Spatial reference system
Cartesian coordinate system that is used to standardize the measurements.
Origin is a position of (x, y, z) = (0, 0, 0)
Define the key terms in linear kinematics and provide examples of each. Terms Definition Equation (if, applicable) Examples Position Location of a point within a reference frame Distance How far the point moved along the path of motion Displacement How far the point moved in a specific direction. (ex. +z upward) Speed How fast the point moved along the path of motion
Speed = Distance/
Change in time
Velocity How fast the point moved in a specific direction. (ex. +z upward)
Velocity = Displacement/
Change in time
Acceleration A rate of change in velocity^
Acceleration = Change in
velocity/ Change in time
Describe the difference between distance and displacement. o Distance is the length of the path. o Displacement is length in a specific direction.
Describe the difference between speed and velocity. o Speed: how fast something moves. o Velocity: is speed with direction. Calculate the linear kinematics variables. o A hiker walked 2000m up the hill over 90min and climbed over 100m. Calculate/identify the following. a. Distance hiker traveled during the hike. b. Vertical displacement of the hiker during the hike. c. The average speed of the hiker during the hike (m/s). d. The average vertical velocity of the hiker during the hike (m/s). (Answer: a. 2000m, b. 100m, c. 0.37m/s, d. 0.019m/s) o The speed skater was moving at 3m/s, 0.5s after leaving the start line, and at 10m/s, 2s after leaving the start line. During the last 5 seconds of the race, the speed dropped from 10m/s to 9m/s. Calculate/identify the following. a. The acceleration of the skater during the first 0.5s. b. The acceleration of the skater during the first 2s. c. The acceleration of the skater between 0.5-2s after the start. d. The acceleration of the skater during the last 5 seconds of the race. (Answer: a. 6m/s^2 , b. 5m/s^2 , c. 4.7m/s^2 , d. -0.2m/s^2 ) Calculate horizontal and vertical displacement and velocity using sin and cos. o Calculate horizontal and vertical displacement (left) and velocity (right) using sin and cos.
Describe projectile. Describe how initial velocity of the projectile is determined by the projection speed and angle. Describe the effects of projection speed on the size and shape of the parabolic path. Describe the effects of projection angle on the size and shape of the parabolic path. Describe the initial horizontal and vertical velocity of a projectile. Describe the effects of increasing projection speed on the initial horizontal and vertical velocity. Describe the effects of increasing projection angle on the initial horizontal and vertical velocity. Describe the change in vertical and horizontal velocity of a projectile during a flight. Describe the vertical and horizontal velocity of a projectile at the apex. Describe the vertical and horizontal velocity of a projectile just before landing (assuming the equal launch and landing height). Calculate/identify the key projectile parameters based on the initial velocity. o The object was launched with an initial vertical velocity of 5m/s and horizontal velocity of 9m/s. Assume that the release height and the landing height is the same. Identify the following. a. The vertical velocity of the object at the apex.
b. The horizontal velocity of the object at the apex. c. The vertical velocity of the object immediately before landing. d. The horizontal velocity of the object immediately before landing. e. The vertical acceleration of the object. f. The horizontal acceleration of the object. (Answer: a. 0m/s, b. 9m/s, c. -5m/s, d. 9m/s, e. -9.81m/s^2 , f. 0m/s^2 ) Describe the key factors that affect peak height, flight time, and horizontal displacement. Describe strategies to maximize peak height. Describe strategies to maximize flight time. Describe strategies to maximize horizontal displacement. Describe how the optimal projection angle to maximize horizontal displacement is affected by the relative height. Apply the understanding of the projectile motion to the performance in various sports. o Describe practical strategies to increase the following when you are hitting a golf ball. a. Peak height b. Flight time c. Horizonal displacement o Describe practical strategies to increase the following when you are jumping up for a jump in figure skating. a. Peak height b. Flight time
Describe the joint axis/plane/motion and the movements occurring in each plane. Joint axis Plane of motion Examples of motion that occurs around the axis Medial-lateral Anterior-posterior Longitudinal Define the key terms in angular kinematics and provide examples of each. Terms Definition Equation (if, applicable) Examples Angular distance Angular displacement Angular speed Angular velocity Angular acceleration Describe the difference between angular distance and displacement. Describe the difference between angular speed and velocity. Describe the difference between average and instantaneous angular speed/velocity. Calculate/identify angular displacement, velocity, and acceleration. o The knee was flexed 80º at the beginning of the kicking motion and extended 70º over
0.05s. As a result, the knee angular velocity increased from 0/s to 600/s.
Calculate/identify the following.
a. Angular displacement at the knee joint over 0.05s b. Average angular velocity (knee extension velocity) over 0.05s in º/s c. Instantaneous angular velocity 0.05s into the kicking motion d. Average angular acceleration over 0.05s
(Answer: a. 70º into extension, b. 1400 º/s into extension, c. 600/s, d. 12000/s^2 )
Describe the phases of movement (ex. throwing) with + and - angular acceleration. Describe the relationship between the angular displacement of an object and the linear displacement of the point on the object. Describe radial and tangential directions for the points on an object going through angular motion. Describe tangential displacement, velocity, and acceleration. Describe how the angular motion (displacement, velocity, and acceleration) of an object relates to the linear motion in the tangential direction (tangential displacement, velocity, and acceleration). Calculate the linear motion in the tangential direction (tangential displacement, velocity, and acceleration) produced by the angular motion (displacement, velocity, and acceleration). o The golf club is rotating at an angular velocity of 4000 º/s (69.8rad/s) and accelerating at 400º/s^2 (7.0rad/s^2 ). The club head is 1.2m away from the axis of rotation. a. Calculate the tangential velocity of the club head. b. Calculate the tangential acceleration of a club head. (Answer: a. 83.8m/s, b. 8.4m/s^2 ) Describe the advantage of having a longer limb in daily activities and sports based on the relationship between linear and angular motion.
o The golf club is rotating at an angular velocity of 4000 º/s (69.8rad/s) and accelerating at 400º/s^2 (7.0rad/s^2 ). The club head is 1.2m away from the axis of rotation. Calculate the radial acceleration of the club head at this time. (Answer: 5846.4m/s^2 ) Calculate radial acceleration of an athlete/object turning a corner. o The speed skater A entered the corner (r=40m) with a linear velocity of 12m/s, and the speed skater B entered the corner (r=45m) with the same linear velocity (12m/s). a. Describe how the linear velocity and rotation radius (r) of the skater affect the radial acceleration of the skater. b. Describe the factors that affect the centripetal force the skater needs to produce to stay in the rotating path. c. Describe what skaters can do to increase the centripetal force. d. Describe what happens to the skaters if they cannot produce enough centripetal force. a. Calculate the magnitude of the radial acceleration of the skater A when he entered the corner. b. Calculate the magnitude of the radial acceleration of the skater B when he entered the corner. (Answer: e. 3.6m/s^2 , f. 3.2m/s^2 )
