L13;C11 Flashcards
What is angular motion?
This is motion about an axis of rotation
What is an axis of rotation?
This is the line that is perpendicular to the plane in which the rotation occurs
What kind of motion can you have with curves and angles?
Linear and angular
Provide me the definitions of the following:
Angular displacement
Angular distance
Angular velocity
Angular acceleration
Angular displacement= change from initial position to final angular position
Angular distance= total distance of angular change. The sum of distance traveled
Angular velocity= change in angular position over a given time
Angular acceleration= change in angular velocity over a given time
True or false, angles are considered a unit. Support your answer.
False, angles are unit-less. They are measured in relation to circles. An angle is measured as its ratio of arc length and radius.
What are the formulas for measuring an angle in:
Rads
Rev
Deg
Rads- θ=s/r
Rev- θ=(s/r)(1/2pi)
Deg- θ= (s/r)(360/2pi)
How much does 1 radian equal in degrees?
57.3 degrees
True or false: radians are dimensionless
True
At 180 degrees, how many rads and revs is that equivalent to? If you want to add to each factor, how much do you do it by?
180=Pi rads= 1/2 rev
You ADD 90 degrees to 180, add Pi/2 to rads and 1/4th to your revs
If reference axis is fixed, than angular position is _________
If reference axis is capable of moving, than angular position is ______
Absolute, relative
Segment angles are ______
Joint angles are _______
Absolute, relative
What is angular distance? What kind fo quantity is it and what is it measured in?
Angular distance (ϕ) is the sum of all angular change undergone by a rotating object. This has no associated direction and is a scalar quantity. Measured in rads, degs, revs
What is angular displacement? Webcast it formula and quantity of measurement?
This is the change in angular position from θ2-θ1 of a rotating object. This is defined as using magnitude and direction and is a vector quantity.
Clockwise motions are ______
Counterclockwise motions are ________
Negative, positive
What is angular velocity? What is its formula? What kind of quantity is it?
Angular velocity is the change in displacement (θ) over the change in the time interval. The formula is:
ω= Δθ/ΔT
This is a vector quantity since it has specified direction and magnitude
What is angular speed? What is its formula? What kind of quantity is it?
Angular speed is the angular distance/amour of time it took to cover that distance.
Angular distance has no associated direction, therefore angular speed is a scalar quantity.
What is angular acceleration? What’s it formula and quantity of measurement? Can the direction be positive, negative or zero?
Angular acceleration is the change in angular velocity (Δω) over a given time (ΔT). This is a vector quantity and its formula is:
α = Δω/ΔT
The direction can be positive, negative, and zero depending on motion and change in velocity
_______ ________ is angular motion about an axis that is OUTSIDE the rotating object
________ ________ is angular motion about an axis at INFINITE distance from a rotating object
Curvilinear motion
Rectangle motion
Curvilinear motion of a point can be related to angular motion of an object using the following formula:
S=rϕ
This must be in radians are S and r must be the same units
The larger the radius of rotation, the greater the ________ _______ traveled by a point on a rotating body
Curvilinear distance
What dictates the connection between the angles and the distance?
The radius
Longer distances= longer ____
Arc
What is the formula for calculating linear velocity of a point rotating around an axis of rotation?
Vt= rxω
When an object travels in a circular path, what is the radial velocity? Why?
Vr=0
When it travels around a circle, the radius’ velocity has to be zero or else the path would not be a perfect circle; since the velocity would be changing the displacement over time
The transverse axis is perpendicular to what axis? What is it parallel to?
The transverse axis is perpendicular to the radial axis and is parallel to the tangent line when the motion path is circular
What factor both relates linear and angular velocity to linear and angular displacement?
The radius
Explain what the transverse component of acceleration (αt) is and its formula.
The transverse component is the acceleration factor that represents the rate of change of linear speed:
αt= Δv/ΔT m/s^2
What can the transverse acceleration be related to? Provide formulas to explain.
Transverse acceleration (αt) can be related to angular acceleration (α)
αt=rxα [ if ω does not equal 0 and α does not equal 0]
αt=0 [if ω is constant and α =0]
Explain the radial component of acceleration (αr)
This represents a change in direction, this is refereed to the centripetal acceleration
αr=Vt^2 [m/s^2]
OR
αr= rxω^2
