Chapter 10: Rotational Variables Flashcards
What is angular position?
The angle between the reference line on a rotating body and a fixed 0 line.
SI unit: radian (rad)
When Θ > 0, the rotation is ___; when Θ < 0, the rotation is ___.
Counterclockwise; clockwise.
Cartesian coordinates are…
Coordinates using standard x and y values on an x and y plane.
Is angular position a vector quantity?
Yes!
Polar coordinates are…
Coordinates organized as (r, Θ), with r being the radius of the circle and Θ being the angle with the x-axis zero position.
Definition of an angle in radians:
Θ = s/r, with s being the arclength and r being the radius.
The radian is a ___ quantity.
Dimensionless
Θ = 2πr/r = …
2πrad = 360° = 1 revolution
What is angular displacement?
The change in angular position.
SI unit: radian (rad)
What is angular velocity?
The rate of change of angular position.
SI unit: rad/s
Is angular displacement a vector quantity?
Yes!
Is angular velocity a vector quantity?
Yes!
What is angular acceleration?
The rate of change of angular velocity.
SI unit: rad/s^2
The rotational motion version of linear constant acceleration equation Δv = aΔt is:
Δω = αΔt
The rotational motion version of linear constant acceleration equation Δx = v(subo)Δt + 0.5a(Δt)^2 is:
ΔΘ = ω(subo)Δt + 0.5α(Δt)^2
The rotational motion version of linear constant acceleration equation v^2 = v(subo)^2 + 2aΔx is:
ω^2 = ω(subo)^2 + 2αΔΘ
Angular variables describe ___, while linear variables describe ___.
A rotating rigid body as a whole; a point on the body.
|v(arrow)| = …
r|ω|
a(subr) = …
r|ω|^2
a(subt) = …
r|α|
Radial acceleration (a(subr)) is…
Acceleration that goes towards the center of the circle, following the radius.
Tangential acceleration (a(subt)) is…
Acceleration that is perpendicular to the radius.
Pure translation is…
Motion in which all points have the same linear velocity.
The kinetic energy of pure translation can be described as…
K(subtrans) = 0.5Mv(subCOM)^2
Pure rotation is…
The rotation of an object when the velocity of the COM is zero.
The kinetic energy of pure rotation can be described as…
K(subrot) = 0.5I|ω|^2
Rotational inertia (I) is…
A measure of how difficult it is to change an object’s angular velocity about a specified axis.
SI unit: kg * m^2
What is the parallel axis theorem?
The rule that specifies how to calculate the rotational inertia of an object when it rotates on an axis parallel to that going through the COM.
I(subp) = I(subCOM) + Mh^2
What is torque (τ)?
A measure of a force’s ability to cause rotation about an axis.
SI unit: Nm
τ = |r||F|sinϕ
A torque that causes clockwise motion is (positive)/(negative), and a torque that causes counterclockwise motion is (positive)/(negative).
Negative; positive.
Torque (is)/(is not) a vector quantity.
Is!
Newton’s second law for rotational motion:
τ(subnet) = Iα
Both net torque and rotational motion must be calculated around the same…
Axis of rotation.
The second law of rotational motion requires that ___ and ___ be in the same direction.
τ(subnet); α.
The no-slipping condition states that:
a(suby) = a(subt)
