Angular Kinematics Chapter 6 KINE 3301 Biomechanics of Human Movement

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 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.

Angular Acceleration Angular acceleration is the rate of change in angular velocity. The units for angular acceleration are r/s 2. 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.

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 a c and a T are m/s 2.

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/s 2. 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/s 2.

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 track athlete increases her velocity from V i = 7.8 m/s to V f = 8.4 m/s in a time of 0.8 s, what was the tangential acceleration ( a T )? 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.