angular kinematics
TRANSCRIPT
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