Dynamics – Study Materials

Based On

ENGR 2030 ENGR 2030 – Engineering Mechanics Dynamics

Format

  • Closed book, closed notes.
  • Calculator permitted.
  • A packet of nates will be given to you at the exam.

Notes are available for your reference while you study. See the GPC for a copy. Otherwise, they will be given to you at the exam.

Advice

Students are responsible to understand the following materials.

Fundamental Abilities.

  • Know how to draw and label a free-body diagram. Be able to show all the forces resolved into the appropriate coordinate directions.
  • Be very proficient at finding the components of a vector in alternate coordinates.
  • Be able to use mass in English units. Know when to divide the mass by the conversion factor of 32.2 (lbm-ft/s2) / lbf.
  • Know how to apply the appropriate relationships to the problems. Understand that when solving a problem, the symbolic form of the appropriate relationship should first be written. Next the actual forces, work, energies, or accelerations should be substituted symbolically. Finally, the numerical values are substituted in and calculations performed.
  • Know how static and dynamic friction forces are applied.

Particle Kinematics.

  • Know what the word kinematics means.
  • Be able to define what a particle is and how that it affects its inertia.
  • Know how to find position, velocity and acceleration from expressions as a function of time and position.
  • Know how to solve problems in rectilinear or curvilinear motion where the acceleration, velocity and/or position are known.
  • Know how the graphs of position, velocity, and acceleration as function of time can be found from one another.
  • Know how the graphs of velocity and acceleration as function of position can be found from one another.
  • Know how to find the motion of a projectile in a constant gravitational field.
  • Know how solve for curvilinear motion in normal and tangential coordinates.
  • Be able to solve for curvilinear motion in cylindrical coordinates.
  • Be able to find the dependent motion of two connected particles.
  • Understand the relationship between two using translating axes.

Particle Kinetics.

  • Know how to use the units of mass in both SI and English units.
  • Understand how to apply Newton’s 2nd law in rectangular, normal-tangential, and cylindrical coordinates.

Work & Energy of a Particle.

  • Be able find the work done by a force. Understand that the force and the displacement must be in the same direction when calculating the work.
  • Know how to find the work done by a a) constant force, b) a spring, c) by weight, and d) by friction.
  • Be able to find the work done by a variable force if the function is known or if given graphically.
  • Starting with Newton’s 2nd law, be able to derive the expression .
  • Be able to find the kinetic energy, T2, knowing the work performed on a particle or system of particles and given the initial kinetic energy, T1.
  • Know what conservative forces are.
  • Be able to find the potential energy from elastic members (springs) and due to gravity.
  • Understand that energy is conserved and can be used to relate the sum of the kinetic and potential energies of a system of particles in state 1 to the sum of the kinetic and potential energies in state 2.

Impulse and Momentum of a Particle.

  • Beginning with Newton’s 2nd law, be able to derive the linear impulse and momentum equation.
  • Know what linear impulse is and how you evaluate the expression when the force is known as a function of time.
  • Know what linear momentum is and to calculate it.
  • Understand how to apply conservation of linear momentum and when it is valid to use.
  • Be able to find the velocities of two particles that collide when their initial velocities are known and either a) they stick together, b) energy is conserved in the collision, or c) the relative velocities of the two particles are known as they separate.
  • Know what non-impulsive forces are and why we can neglect them in impulse momentum calculations.
  • Understand what impact is and what makes it a special case of impulse. Know the difference between central and oblique impact.
  • What is the coefficient of restitution and what does it mean when e=1 and when e=0.
  • Know how angular momentum is defined and what the units are of angular momentum.
  • Be able to calculate the angular momentum when the linear momentum and the moment arm are perpendicular (dmv).
  • Be able to find the cross product of the moment arm, r, and the linear momentum to find the angular momentum.
  • Know what the relationship is between the moment of a force on a particle and the time rate of change angular momentum. Be able solve problems with this relationship.
  • Know how to calculate the angular impulse. Know how to calculate a moment.
  • Be able to solve problems using the angular impulse and momentum expression.
  • Know when to use the conservation of angular momentum expression.

Planar Kinematics of a Rigid Body.

  • Know the relationships between . Know how to use these relationships when the acceleration is constant.

Additionally

  • Be able to find the velocity of a point on a rigid body that is rotating about a fixed point.
  • Be able to find the normal acceleration of a point on a rigid body that is rotating about a fixed point.
  • Be able to find the tangential acceleration of a point on a rigid body that is rotating about a fixed point.
  • Be aware that to rigid bodies in contact as they rotate about fixed point have the same velocity at the contact point but not necessarily the same accelerations at the contact point.
  • Be able to use the chain-rule to solve problems using absolute motion analysis.
  • Know how to find the velocity of a point B on a rigid body with respect to a point A on the rigid body.
  • Know how to find the acceleration of a point B on a rigid body with respect to a point A on the rigid body.

Planar Rigid Body Kinetics.

  • Know how the mass moment of inertia is defined.
  • Know how to find the mass moment of inertia for a compound body.
  • Know how to find the mass moment of inertia about another axis using the parallel-axis theorem.
  • Be able to find the center of mass of a planar rigid body.
  • Know how the radius of gyration is defined.
  • Know how to solve problems using the equations of motion for a planar rigid body in general motion.
    • Know how to solve problems when summing moments about the center of mass. No translational inertia terms are used.
    • Know how to solve problems when summing moments about a point other than the center of mass. Sliding inertial moments are included.
  • Know how to solve problems using the equations of motion for a planar rigid body rotating about a fixed point.
    • Know how to solve problems when summing moments about the center of mass.
    • Know how to solve problems when summing moments about a point other than the center of mass.

Work and Energy of a Rigid Body.

  • Be able find the work done by a moment.
  • Know how to find the kinetic energy of a rotating and translating rigid body.
  • Be able to find the kinetic energy, T2, knowing the work performed on a rigid body and given the initial kinetic energy, T1.
  • Be able to find the potential energy from elastic members (springs) and due to gravity.
  • Know how to use the conservation energy to solve dynamic problems of planar rigid bodies.

Impulse and Momentum of a Rigid Body.

  • Know what linear impulse and angular impulse are and how to calculate them for a rigid body in a) general planar motion, b) translating, and c) about a fixed point.
  • Know what linear momentum and angular momentum are and how to calculate them for a rigid body in a) general planar motion, b) translating, and c) about a fixed point.
  • Understand how to apply conservation of angular momentum and when it is valid to use.
  • Know how angular momentum is defined and what the units are of angular momentum.