Angular Kinematics: Equilibrium and Torque

Question 1

Identify and define static, and dynamic equilibriums.

Answer 1

Static equilibrium
- the net external forces in all directions acting on a
system is zero (x- & y-axis included)

Dynamic equilibrium
- the net external forces acting on a system moving from all directions with constant velocity are zero

Two conditions must be met to be in true equilibrium:
1. Net forces must equal zero
2. Net torques must equal
zero

Question 2

Calculate systems that are in various states of equilibrium

Answer 2

Three types of systems in equilibrium:
1. Stable equilibrium
- Restoring force to
displacement

2. Unstable equilibrium
   - Displacement beyond restoring force
3. Neutral equilibrium
   - Independant from displacement

Question 3

Identify and provide examples of how to improve stability in a system

Answer 3

Strategies to become more stable:
- Lower
- Wider

Question 4

Define torque, and identify it in illustrations.

Answer 4

Torque (𝛕):
- Is directly proportional to the force (F) and
length from the axis point of rotation where the force is applied (r) relative to the angle (𝝷) of which the force is applied
- Vector (magnitude and direction)
- Clockwise (CW) or counter-clockwise
(CCW)
- Torque is rotations’ equivalent of translational
force.
𝛕 = I𝞪 (F=ma)
- I is the moment of inertia
- For a mass point I = mr2 (more later on
this)
- SI Units = N*m = Nm

Question 5

Understand how to apply the concept of torque and it’s variables to unique scenarios

Question 6

Calculate torque, including in equilibrium settings.

Question 7

Define and identify moment of inertia, and know how it relates to rotational mass

Answer 7

Moment of Inertia (I):
- Is directly proportional to the
sum of the mass of all parts of an object (mi) and distance from the axis of rotation (r)
- “Rotational mass”
- Capacity to resist inertia
- ‘Mass point’ assumes thread (r) is
negligible in its mass.
- SI Units = kg*m2

Question 8

Understand the concept of moment of inertia, and how to apply changes in variables (mass and radial arm).

Question 9

Define, calculate, and apply the concept of angular momentum.

Answer 9

Angular Momentum (L)
- Is directly proportional
to the moment of inertia (I) and the angular velocity (ω) of an object rotating around its axis.
- Is conserved for any system (first state or position = second state or position)
- SI Units = kg*m2/s