11.1 - Rotational Dynamics

• What is the moment of inertia for an isolated point mass?

  A measure of how difficult it is to alter an object's rotational speed:

  
  

  I = mr^2

  I = Moment of inertia

  m = mass

  r = distance from axis of rotation
• What is the moment of inertia of an extended object?

  I = sum of mr^2

  Add the individual moments of inertia for each point mass that makes up the object
• Is a small mass m is added to a rod at radius r from the axis of rotation, what is the new moment of inertia?

  I new = I initial + mr^2

  Where mr^2 is the moment of inertia for the small mass added
• What affects of the moment of inertia of a rotating object?

  The mass and mass distribution of the object, the position of the axis of rotation, and how far away the mass is from it
• What is the rotational kinetic energy of an object?

  
• What is torque?


  A measure of how much a force causes an object to rotate about an axis measured in Nm
• What is a flywheel?

  Flywheels are heavy wheels with a high moment of inertia and angular momentum that convert inputted torque to rotational kinetic energy. They are used to store energy in a machine to be used at another point in a system.
• What factors affect the energy storage capacity of a flywheel?


  Shape and mass: Increased moment of inertia, increased kinetic energy. Flywheels shaped as wheels instead of discs can store more energy if r is greater. Spoked wheels store more energy

  Material: Max angular velocity is restricted by the breaking stress of the flywheel, higher angular velocity, higher kinetic energy
• How are flywheels used for storing energy in braking vehicles?

  Electric vehicles use regenerative braking. When the brakes are applied, a flywheel is engaged, which charges up with the energy being lost. The energy is used to move the wheels when the vehicle accelerates and is then disengaged
• How are flywheels used for smoothing torque and angular velocity?

  Flywheels use each burst of power to charge and then smoothly deliver the energy to the rotating components. For systems that exert a varying force when the load torque is too high, the flywheels decelerates to top up the system and vice versa when the engine torque is higher than the load torque
• How are flywheels used in production processes?

  Most production, such as piercing sheets of metal, require constant uniform action. Attaching a flywheel to the motor reduces problems by smoothing out fluctuations
• What are the advantages of flywheels?

  ● Very efficient.

  ● Long working life.

  ● Short recharge time.

  ● Environmentally friendly.
• What are the disadvantages of flywheels?

  - larger and heavier than other storage methods

  
  

  - safety risk as wheel could break at high speeds

  
  

  - energy lost through friction

  
  

  - can oppose changes in direction for moving vehicles (but also helps improve stability)
• What is angular displacement?


  The angle through which an object on a circular path moves through, measured in radians
• What is the relation between angular acceleration, angular velocity and angular displacement?

  ⍵ = dθ/dt (where d represents 'change in')

  𝛼 = d⍵/dt

  𝛼 = d2 θ/dt2
• When is angular momentum conserved?

  It is conserved only when no external force acts on the object
• What is angular impulse?

  The change in angular momentum or equivalently a product of a constant torque and time duration of that change
• How does angular impulse relate to torque graphically?

  Angular impulse is the area under the torque-time graph
• How can you calculate the work done when rotating an object?

  Work done = Torque * Angular Displacement
• How can the work done be calculated graphically with a non-constant torque?

  The work done is the area under the torque-angular displacement graph
• Is there a frictional torque when rotating an object?

  Yes, there is a frictional force resisting motion which causes a frictional torque, and some work will need to be expended in overcoming the frictional torque
• How do you convert from rads per second to rpm?

  Multiply by 60/2pi
• How do you convert from rpm to rads per second?

  Multiply by 2pi/60