Mechanics Kinematics Dynamics Mechanics Kinematics Description of how

Mechanics Kinematics Dynamics

Mechanics Kinematics Description of how objects move Dynamics Deals with forces and why objects move as they do

Kinematics Classical Translational Rotational Relativistic

Kinematics Translational (1 -D) x (position) v = dx/dt (velocity) a = dv/dt = d 2 x/dt 2 (acceleration)

Kinematics • Translational (3 -D):

Kinematics How are x, v, a and t related?

Kinematics How are x, v, a and t related? Consider special case with constant acceleration:

Kinematics (a = constant)

Kinematics (a = constant) Always true

Kinematics (a = constant)

Kinematics (a = constant) Always true

Kinematics (a = constant)

Kinematics (a = constant)

Kinematics How are x, v, a and t related when acceleration is NOT constant?

Kinematics How are x, v, a and t related when acceleration is NOT constant? Graphical Approach Analytical Approach

Kinematics (Graphical)

Kinematics (Graphical) Area=Velocity

Kinematics (Graphical)

Kinematics (Graphical) Positive Negative

Kinematics (Graphical)

Kinematics (Graphical) Displacement

Kinematics (Analytical)

Kinematics (Analytical) Not the answer!

Kinematics (Analytical) Do units make sense?

Kinematics (Analytical) Do limits make sense?

Kinematics (Relative Velocity) vws v. BS v. BW

Kinematics (Relative Velocity) v. SB vw. B vsw

Kinematics Classical Translational Rotational Relativistic

Kinematics (Rotational) Direction of angular velocity and angular acceleration is along the axis of rotation and can be determined by the RHR.

Kinematics (Rotational) Angular acceleration is constant

Mechanics Kinematics Dynamics

Dynamics Classical Translational Rotational Relativistic

Dynamics (Translational) Newton’s Laws

Dynamics (Newton’s Laws)

Dynamics (Translational) Conservation of Momentum

Dynamics (Translational) Impulse

Dynamics (Translational) Impulse - Graphical

Dynamics (Translational) Impulse - Graphical +Impulse -Impulse

Dynamics (Translational) Conservation of Momentum and Kinetic Energy

Dynamics Classical Translational Rotational Relativistic

Dynamics (Rotational) Torque: The CAUSE of a change in rotational motion

Dynamics (Rotational) Rotational Inertia

Dynamics (Rotational) Rotational Inertia

Dynamics (Rotational) Rotational Analog to Newton’s Laws

Dynamics (Rotational) Conservation Laws

Dynamics (Work-Energy Principle)

Dynamics (Work)

Dynamics (Conservation of Mechanical Energy)

Kepler’s Laws of Planetary Motion 1 st Law: The path of each planet about the Sun is an ellipse with the Sun at one focus. 2 nd Law: Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time. 3 rd Law: (T 1/T 2)2 = (S 1/S 2)3 where T is the orbital period in years and S is the semi-major axis of the orbit in AU.

Kepler’s Laws of Planetary Motion 1 st Law: The path of each planet about the Sun is an ellipse with the Sun at one focus. Recall this empirical law was derived by Newton using the ULo. G and N 3 L. We did this by solving a general differential equation for the orbit of a particle subject to an inverse square law force.

Kepler’s Laws of Planetary Motion 2 nd Law: Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out equal areas in equal periods of time. Recall that for ALL central forces, angular momentum is conserved. Kepler’s second law is simply a consequence of the conservation of angular momentum for an inverse-square law.

Kepler’s Laws of Planetary Motion 3 rd Law: (T 1/T 2)2 = (S 1/S 2)3 where T is the orbital period in years and S is the semi-major axis of the orbit in AU. Recall that Newton’s version of Kepler’s 3 rd law generalizes to all orbiting pairs of masses and is used frequently in astronomy to determine the mass of a heavier object (planet or star) by measuring the orbital period of a much smaller object (moon, planet, artificial satellite).