ESS 303 – Biomechanics

Angular Kinematics

From Last Time

Someone kicks a football so that it travels at a velocity of 29.7m/s at an angle of 22° above the ground What was the vertical component of velocity? What was the horizontal component of velocity?

SOH (sin of an angle = opposite / hypotenuse) sin 22 = Y / 29.7m/s Y = sin 22 * 29.7m/s = 11.13m/s

CAH (cos of an angle = adjacent / hypotenuse) cos 22 = X / 29.7m/s X = cos 22 * 29.7m/s = 27.54m/s

Angular Kinematics

The branch of biomechanics that deals with the description of the angular components of motion

Uses degrees or radians to describe position and/or movementDegree: 360° in a circleRadian: the length of 1 radius along the arc

of a circle1 radian = 57.3 degrees

Angular Kinematics

In the drawing to the right – A, B & C have the same angular displacement or rotation

A, B & C have different linear displacements

A B C

A B

C

Angular Kinematics

θ = S/R θ = angle in radians S = displacement

along the arc R = radius

If radius A = 1m, radius B = 2m, radius C = 3m and each had a rotation of 90°, what were the displacements of each?

A B C

A B

C

Angular Kinematics

90° = 1.57 radiansSA = 1.57rad * 1mSA = 1.57mSB = 1.57rad * 2mSB = 3.14mSC = 1.57rad * 3mSC = 4.71m

A B C

A B

C

Angle Types

Relative: angle between segmentsAbsolute: describes the orientation of

an object in space

(7,9)

(5,5)

Yproximal - Ydistal

Tan θ = –––––––––––––Xproximal - Xdistal

Femoral Angle = 63.43°

Right Hand Rule

Today’s Formulas

1 radian = 57.3 degrees θ = S/R (remember to use radians here)Tan θ = (Yproximal – Ydistal)/(Xproximal – Xdistal)Angular speed = angular distance/time

Angular velocity (ω) = ∆θ / ∆t

Angular acceleration (α) = ∆ω / ∆t

Problems

A figure skater turns 6 ½ timesWhat was the angular distance traveled?What was the angular displacement?

While watching a golf swing, you note that the angular velocity at time1 (0.05s)

was 6.5rad/s and at time2 (0.54s) was

15.87rad/sWhat was the angular acceleration?