angular kinematics

Describing angular motion or displacement?

Angular Distance and Displacement = angle

Units of measurement• radians (1 rad = 57.3)• degree ()• revolutions (revs)

Describing angular motion or displacement?

Angular Velocity () Time rate of change of angular displacement

(rad/s, deg/s, rev/s)

where linear was v = Δs/t

Angular equivalent =

= Δ/ Δ tWhere:

Δ = change angle

t = time interval

Describing angular motion or displacement?

Angular Acceleration () Time rate of change of angular velocity(rad/s/s,

deg/s/s, rev/s/s)

Where linear was a = Δv/t

Angular equivalent =

= Δ /t

Δ = change angular velocity

t = time interval

Combining Linear and Angular Velocity?

Linear Velocity Endpoint =

Angular Velocity () x Radius of Rotation (r)

You MUST only work in radians when using this formula

to convert

• degrees/ 57.3

Lv = xr

Radius of Rotation? :Golf

Linear Velocity of Vb (end of club)

is greater than Va (for same )

Linxr

Lin

r is larger in Vb so club head

linear velocity is

When a rotating body moves from one position to another, the angular distance through which it moves is equal to the length of the angular path.

Vb

Va

Applied Anatomy: Thigh?

Linear motion of the body is due to angular motion

of segments

Cricket?

In situations where the objects ‘s COM has a linear

velocity it must be added to the equation.

Kicking

vball = vhip + (xr)

Bowling (throwing)

vball = vshoulder + (xr)

Where the shoulder in throwing and the hip in kicking already incorporates

the linear velocity of the COM

Question

Calculate the linear velocity of the throwing-shoulder at release of a discus

thrower , who:

1. Moves across the circle at 1 m/s

2. Rotates the trunk through 360 degrees in 0.2 s

3. The length from the central axis of trunk rotation to the shoulder is

0.25 m

Lecture Outcomes

• What is the equation for calculating angular velocity? Write as an

equation and as a definition.

• Write the equation for the velocity of the ankle joint in a soccer kick

or a netball shot for goal (start the kick at the ankle, which has a

velocity of 2 ms-1 and the netball shot at the shoulder which has

the same velocity).

• Define the angular equivalent of displacement, velocity and

acceleration using formula and words.

Real World Problem

A softballer rotates the bat horizontally at 10 rad/s. If her shoulder is

moving forward at 2m/s and the distance of the point of impact with

the ball and her shoulder is 1m, what is the forward velocity of the end

of the bat at the point of impact?

Real World Problem

A softballer rotates the bat horizontally at 10 rad/s. If her

shoulder is moving forward at 2m/s and the distance of the

point of impact with the ball and her shoulder is 1m, what is the

forward velocity of the end of the bat at the point of impact?

vbat = vshoulder + (xr)

vbat = 2 + (10x1)

12 m/s

Answers

1. Convert degrees to radians

= 360/ 57.3

= 6.28 radians

2. Calculate angular velocity

ω = /t

= 6.28/ 0.2

= 31.4 rad/s

3. Vshoulder = Vcg + (trunk x ltrunk)

= Vcg + (31.4) x (0.25)

= 1 + 7.85 m/s = 8.85 m/s