Download Angular Kinematics

KINE 3301
Biomechanics of Human Movement
Angular Kinematics
Chapter 6
Radian
A radian is a ratio variable. The arc length (s) is
divided by the radius (r).
Segment Angles & Joint Angles
A segment angle is the angle from the
right horizontal to the segment.
A joint angle is the angle
between two segments.
Angular Variables & Right Hand Rule
Right Hand Rule: Curl the fingers of your
right hand in the direction of rotation
and your thumb points in the direction
of the angular motion vector.
Angular Velocity
𝜃𝑓− 𝜃𝑖
𝜔=
𝑡
Angular velocity is the rate
of change of the angular
position, or the slope of the
angle – time curve. The
units for angular velocity are
r/s.
The direction of the angular velocity vector is defined by
the right hand rule.
http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Kine-3301.html
Angular Acceleration
𝜔𝑓− 𝜔𝑖
𝛼=
𝑡
Angular acceleration is the
rate of change in angular
velocity. The units for angular
acceleration are r/s2.
The direction of the angular acceleration vector is defined by the right hand rule.
The relationship between linear and angular velocity is
defined by the equation below. The angular velocity
must be in r/s.
𝑣 = 𝜔𝑟
Tangential & Radial Acceleration
An object rotating has two linear accelerations. Tangential
acceleration is tangent to the path and centripetal acceleration is
directed toward the center of rotation. The units for ac and aT are
m/s2.
Tangential Acceleration
The tangential acceleration represents the acceleration necessary to
change the rate of rotation. It is tangent to the path with units of m/s2.
If the object is rotating at a constant velocity tangential acceleration is
zero.
Centripetal Acceleration
Centripetal acceleration is directed inward towards the center of the circle.
To keep an object rotating in a circle it must be accelerated with a
centripetal acceleration. The units for centripetal acceleration are m/s2.
Centripetal Force
If you multiply the centripetal acceleration by mass you get the centripetal force. The
centripetal force is the force necessary to keep an object rotating in a circle, it has
units of N and like centripetal acceleration it is directed inward toward the center of
the circle.
A volleyball player’s forearm rotates from an
initial angle (𝜃𝑖 ) of .4 r to a final angle (𝜃𝑓 ) of .9 r
in t = .2 seconds, compute the angular velocity
(𝜔).
If the radius r of rotation for the volleyball players
arm about the shoulder is .72 m what is the linear
velocity of the hand?
A baseball player’s forearm rotates from an initial
angular velocity (𝜔𝑖 ) of 1.4 r/s to a final angular
velocity (𝜔𝑓 ) of .9 r/s in t = .2 seconds, compute
the angular acceleration (𝛼).
If the radius r of rotation for the baseball players
arm about the shoulder is .83 m what is the
tangential acceleration (aT)?
Compute the centripetal acceleration (aC) and
centripetal force (Fc) necessary to keep a 2 kg
discus rotating with a radius of 1.3 m and an
angular velocity (𝜔) of 2.2 r/s.
Compute the centripetal acceleration (aC) and
centripetal force (Fc) necessary to keep a 7.257 kg
hammer rotating with a radius of 2.1 m and a linear
velocity (v) of 13 m/s.
What is the angular velocity of the hammer?
A soccer player accelerates the lower leg with an
angular acceleration (𝛼) of −14 r/s2 for t = 0.3
seconds, if the initial angular velocity (𝜔𝑖 ) was
0.3 r/s, what was the final angular velocity (𝜔𝑓 ) ?
Using the final angular velocity (𝜔𝑓 ) above and a
radius of 1.34 m what was the linear velocity of
the foot?
A track athlete increases her velocity from Vi = 7.8
m/s to Vf = 8.4 m/s in a time of 0.8 s, what was
the tangential acceleration (aT)?
Compute centripetal force (Fc) necessary to swing
a 7.6 kg bowling ball with a velocity of 12 m/s and
a radius of 1.2 m.