Chapter 10: Rotational Variables

Question 1

What is angular position?

Answer 1

The angle between the reference line on a rotating body and a fixed 0 line.
SI unit: radian (rad)

Question 2

When Θ > 0, the rotation is ___; when Θ < 0, the rotation is ___.

Answer 2

Counterclockwise; clockwise.

Question 3

Cartesian coordinates are…

Answer 3

Coordinates using standard x and y values on an x and y plane.

Question 4

Is angular position a vector quantity?

Answer 4

Yes!

Question 5

Polar coordinates are…

Answer 5

Coordinates organized as (r, Θ), with r being the radius of the circle and Θ being the angle with the x-axis zero position.

Question 6

Definition of an angle in radians:

Answer 6

Θ = s/r, with s being the arclength and r being the radius.

Question 7

The radian is a ___ quantity.

Answer 7

Dimensionless

Question 8

Θ = 2πr/r = …

Answer 8

2πrad = 360° = 1 revolution

Question 9

What is angular displacement?

Answer 9

The change in angular position.
SI unit: radian (rad)

Question 10

What is angular velocity?

Answer 10

The rate of change of angular position.
SI unit: rad/s

Question 11

Is angular displacement a vector quantity?

Answer 11

Yes!

Question 12

Is angular velocity a vector quantity?

Answer 12

Yes!

Question 13

What is angular acceleration?

Answer 13

The rate of change of angular velocity.
SI unit: rad/s^2

Question 14

The rotational motion version of linear constant acceleration equation Δv = aΔt is:

Answer 14

Δω = αΔt

Question 15

The rotational motion version of linear constant acceleration equation Δx = v(subo)Δt + 0.5a(Δt)^2 is:

Answer 15

ΔΘ = ω(subo)Δt + 0.5α(Δt)^2

Question 16

The rotational motion version of linear constant acceleration equation v^2 = v(subo)^2 + 2aΔx is:

Answer 16

ω^2 = ω(subo)^2 + 2αΔΘ

Question 17

Angular variables describe ___, while linear variables describe ___.

Answer 17

A rotating rigid body as a whole; a point on the body.

Question 18

|v(arrow)| = …

Answer 18

r|ω|

Question 19

a(subr) = …

Answer 19

r|ω|^2

Question 20

a(subt) = …

Answer 20

r|α|

Question 21

Radial acceleration (a(subr)) is…

Answer 21

Acceleration that goes towards the center of the circle, following the radius.

Question 22

Tangential acceleration (a(subt)) is…

Answer 22

Acceleration that is perpendicular to the radius.

Question 23

Pure translation is…

Answer 23

Motion in which all points have the same linear velocity.

Question 24

The kinetic energy of pure translation can be described as…

Answer 24

K(subtrans) = 0.5Mv(subCOM)^2

Question 25

Pure rotation is…

Answer 25

The rotation of an object when the velocity of the COM is zero.

Question 26

The kinetic energy of pure rotation can be described as…

Answer 26

K(subrot) = 0.5I|ω|^2

Question 27

Rotational inertia (I) is…

Answer 27

A measure of how difficult it is to change an object’s angular velocity about a specified axis.
SI unit: kg * m^2

Question 28

What is the parallel axis theorem?

Answer 28

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

Question 29

What is torque (τ)?

Answer 29

A measure of a force’s ability to cause rotation about an axis.
SI unit: Nm
τ = |r||F|sinϕ

Question 30

A torque that causes clockwise motion is (positive)/(negative), and a torque that causes counterclockwise motion is (positive)/(negative).

Answer 30

Negative; positive.

Question 31

Torque (is)/(is not) a vector quantity.

Answer 31

Is!

Question 32

Newton’s second law for rotational motion:

Answer 32

τ(subnet) = Iα

Question 33

Both net torque and rotational motion must be calculated around the same…

Answer 33

Axis of rotation.

Question 34

The second law of rotational motion requires that ___ and ___ be in the same direction.

Answer 34

τ(subnet); α.

Question 35

The no-slipping condition states that:

Answer 35

a(suby) = a(subt)