Chapter 6 - Angular Kinematics Flashcards
(21 cards)
What is angular kinematics?
Describes angular motion
What is absolute angular position? Example.
if other line or plane is fixed and immovable relative to the earth
*external reference direction, “total” angle measures, like a rotating wheel marked point at its absolute angular position
What is relative angular position? Example.
if other line or plane is capable of moving
*its change in angle from a previous or starting position
- wheel rotated from 90 to 150 degress
How do you find an angle usually in angular kinematics?
𝜃 = arc length/r = l/r
What are a units of a circle. Think about the conversions.
360/circle = 2pie/circle = 6.28 rad/circle
What is angular displacement? What are different formulas used?
Angular displacement is the change in the angular position over time
Formula -
θ displacement =θ final − θ initial
θ = 35 - 5 = +30
arc length = θ = s/r
*or a change in absolute angular position experienced by a rotating line
- absolute is the angle measured from a fixed reference direction (like a coordinate axis) rather a relative angle between two lines
What is angular velocity? What are the units?
rate of change of angular displacement. (with time)
* or describe how fast something is rotating and in which direction
Units: rad/s or degrees/sec or rpm (revolutions per minute)
What is the formula for average angular velocity?
ω= dθ/dt
w = angular velocity
t= time
*you can find deltaθ from θf - θi/ dt
What is instantaneous angular velocity?
How fast something is rotating at a specific instant in time
*example: t = 3s
What is angular acceleration? what are the units?
Rate of change of angular velocity
Units: rad/s/s or rad/s^2 or degress/s^2
What is the formula for angular acceleration?
𝛼 = ∆𝜔/ deltaT = 𝜔f - 𝜔i/ deltaT
When does angular acceleration occurs?
When something spins faster and faster or slower and slower, or when spinning object’s axis of spin changes direction
How do sports manipulate the relationship between linear and angular velocity?
vT=ωr
When a bat or a club rotates, the end (where the ball is hit) travels faster than the hands holding it
- This is because the linear (tangential) velocity increases with radius (r)
- The farther from the axis or rotation, the faster the point moves
How is linear and angular velocity used in golf clubs and baseball bats? (bunts vs. Home runs swing) In terms of length or types of swings?
Longer clubs or bats = greater r (r) = greater linear velocity vT at the striking point
- helps transfer more energy to the ball for longer shots or hits
- shorter club (like wedges) has smaller r, giving players more control but less power
Bunts vs Home Run Swings
Bunt: the bat is held still - little or no angular velocity (w = 0
Home run swings: rotate the ball quickly - high w
- the ball hits near the end of the bat - large r
high w + large r = high hT
What is tangential acceleration?
Component of linear acceleration tangent to the circular path of a point on a rtotating object
*describes how fast the linear (tangential) speed of rating object is changing
What is the formula for tangential acceleration?
a T = dVt/ dT
Vt = linear velocity
or VT = wr, and if w is changing
aT = r x a
r = radius (m)
a = angular acceleration (rad/s^2)
aT - tangential acceleration (m/s^2)
What happens to aT when the object is rotating at a constant angular velocity?
aT = 0
* aT tells us how quickly the linear speed (Vt) of a rotating object is changing
- if w is not changing then,
dw/dt = 0 so,
aT = r x a = r x 0 = 0
What are examples of tangential acceleration?
- when a pitcher speeds up their arm in throwing motion
- when a car speeds up while turning in a curve
- last one is both centrpetal and tangential acting on it
What is another way to write tangential acceleration?
aT = dvT/dt , VT = wr > aT = r x dw/dt = r x a
What is centripetal acceleration?
linear acceleration directed toward the axis of rotation
What is the difference between tangential acceleration and centripetal accleration? (aT vs. aC)
aT: change in speed along the circular path
aT = ra
Exists when: the object is speeding up or slowing down
aC: change in direction of velocity toward the center
aC = V^2/ r or aC = rw^2
Exists when: the object is moving in a circular path.
