Chapter 5 - Angular Kinematics Flashcards
What is a relative angle?
Relative angle is the angle at a joint formed between the longitudinal axes of adjacent body segments also known as joint angle.
The straight, fully extended position at a joint is regarded as zero degrees
What is the straight, fully extended position at a joint regarded as?
Zero degrees
Angle at a joint formed between the longitudinal axes of adjacent body segments also known as joint angle the straight, fully extended position at a joint is regarded as zero degrees. True or False?
True.
What is an absolute angle?
Absolute angle is the angular orientation of a body segment with respect to a fixed line of reference. The reference lines are usually vertical or horizontal.
What is angular displacement?
Angular displacement is the change in angular position.
It is also known as the directed angular distance from initial to final angular position
The vector equivalent of angular distance.
What are the units for angular displacement?
It is measured in units of degrees, radians or rotations
What is a radian?
The size of the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
How many degrees and radians is 1/4 revolution?
90 degrees
π/2 radians
How many degrees and radians is 1/2 revolution?
180 degrees
π radians
How many degrees and radians is 3/4 revolution?
270 degrees
3π/2 radians
How many degrees and radians is 1 revolution?
360 degrees
2π radians
What is angular velocity?
It is the rate of change in angular position
Formula for angular velocity?
angular velocity = angular displacement/time
ω = θ / t
What are the units for angular velocity?
degrees/s or radians/s
What is angular acceleration?
Angular acceleration is the rate of change in angular velocity
What is the formula for angular acceleration?
angular acceleration = Δ angular velocity/time
α = ω2 - ω1 / t
What is the unit for angular acceleration?
Angular acceleration is measured in units of deg/s or rad/s
Question example:
A golf club is swung with an average angular acceleration of 1.5rad/s^2. What is the angular velocity of the club when it strikes the ball at the end of a 0.8-s swing? (Provide an answer in both radian and degree-based units.)
Acceleration = ω2 - ω1 / t
1.5rad/s^2 = ω2 - ω1 / 0.8
(1.5rad/s^2)(0.8s) = ω2 - 0
ω2 = 1.2 rad/s
In degree-based units:
ω2 = (1.2rad/s)(57.3deg/rad)
ω2 = 68.8 deg/s
What is the relationship between linear and angular displacement?
The greater the radius between a given point on a rotating body and the axis of rotation, the greater the linear distance traveled by that point during an angular motion.
What is the relationship between linear and angular motion?
The larger the radius of rotation (r), the greater the linear distance (s) traveled by a point on a rotating body.
s = rθ
where θ is the angular displacement in radians.
What is the relationship between linear and angular velocity?
Since velocity is displacement over time, linear and angular velocity are related by the same factor that relates displacement: the radius of rotation (r).
v = rω
Question example:
Two baseballs are consecutively hit by a bat. The first ball is hit 20cm from the bat’s axis of rotation, and the second bat is hit 40cm from the bat’s axis of rotation. If the angular velocity of the bat was 30rad/s at the instant that both balls were contacted, what was the linear velocity of the bat at the two contact points?
v = rω
For ball 1:
v1 = (0.20m)(30rad/s)
v1 = 6m/s
For ball 2:
v2 = (0.40m)(30rad/s)
v2 = 12m/s
What is the relationship between linear and angular acceleration?
The acceleration of a body in angular motion can be resolved into two perpendicular linear acceleration components
What is tangential acceleration?
Tangential acceleration is the component of acceleration of angular motion directed along a tangent to the path of motion.
It represents the change in linear speed.
at = v2 - v1 / t
What is radial acceleration?
Radial acceleration is the component of acceleration of angular motion directed toward the center of curvature.
It represents change in direction.
ar = v^2/r
Question Example:
A windmill-style softball pitcher executes a pitch in 0.65s. If her pitching arm is 0.7m long, what are the magnitudes of the tangential and radial accelerations on the ball just before ball release, when tangential ball speed is 20m/s? What is the magnitude of the total acceleration on the ball at this point?
t = 0.65s
r = 0.7m
v2 = 20m/s
To get tangential acceleration:
at = v2 - v1 / t
Assuming v1 = 0,
at = 20m/s - 0 / 0.65s
at = 30.8m/s^2
To get radial acceleration:
ar = v^2/r
ar = (20m/s)^2 / 0.7m
ar = 571.4m/s
To get total acceleration, perform vector composition of tangential and radial acceleration. Because tangential and radial acceleration are oriented perpendicular to each other, the Pythagorean theorem can be used to calculate the magnitude of total acceleration.
Total acceleration =
√(30.8m/s^2)^2 + (571.4m/s^2)^2 = 572.2m/s^2
Hence, a = 572.2m/s^2