Curvilinear motion Flashcards
What is curvilinear motion?
A particle moving along a curved path undergoes curvilinear motion.
- Vectors are used to describe the motion
- Curve is defined by the path function, s.
- Both the magnitude and the direction of r may vary with time.
What is the general curvilinear motion equations for position, displacement, velocity and acceleration? Think about instaneous and average values. What are there general directions of motion?
Hint: What is the general equation, essentially.
How do we describe curivlinear motion using rectangular coordinates?
We use vectors (the x,y,z or rectangular components) and a fixed coordinate system to relate how the object moves through space and time. Each x, y and z component may be time dependent. I.e. x = x(t), y = y(t), z = z(t).
What is the equation for a particles position using rectangular coordinates, for curvilinear motion? What is the magnitude and the direction of the unit vector of that position vector?
What are the equations and the magnitudes of velocity and acceleration vectors for rectangular coordinates, for curvilinear motion?
What are the three equations of motion in cartesian coordinates?
Hint: think newtons second law in 3D.
True or false:
Projectile motion can’t be treated as two rectilinear motions. They depend on each other.
False.
- Horizontal motion stays constant
- Verticle motion is the only thing that changes, but with constant acceleration (g).
What are the kinematic equations for displacement and velocity for both horizontal and vertical directions of a projectile?
What is the equation for obtaining trajectory path, y(x), for a projectile?
Can you derive it from the two funamental projectile equations
What is the equation for time of flight, t_f, for a projectile?
Can you derive it from the two funamental projectile equations
What is the equation for horizontal distance, y_0, for a projectile?
Can you derive it from the two funamental projectile equations
What are the effects of adding drag to projectile motion?
When would we use normal & tangential components (n-t coordinates), for curvilinear motion?
What are the features of an n-t coordinate system
- Use this when the path of the motion is known.
- The origin is located on the particle.
- The origin moves with the particle and its position is defined from a fixed point on the path O.
What do each of these parameters mean on an n-t coordinate system?
What is the equation for velocity and acceleration using an n-t coordinate system?
What is the equation for the radius of curvature, ρ, for an n-t coordinate system?
What do we change about an n-t coordinate system for 3D motion? What are the conditions for this to apply?
- Use an n-t-b system
- b stands for binormal direction.
- There is no motion in the binormal direction.
What are the equations for position, velocity and acceleration for n-t coordinate systems for circular paths?
How are angular kinematic equations related to rectilinear kinematic equations?
They can be thought of as almost identical. We can relate the two equations. Both for constant acceleration and not. See below.
What are the equations for finding the relative position, velocity and acceleration of two particles, A and B?
What are the two ways to solve relative motion problems?
Relative motion equations are vector equations. They can be solved in two different ways:
* Using cartesian vectors and the resulting 2-D scalar component equations solved for up to two unkowns.
* You can solve graphically using trigonometry. Using laws of sine and cosine.
What is the law of sines and cosines?
What are the equations of motion in cartesian coordinates?
What are the equations of motion for a curvilinear motion using n-t-b coordinates?
- Centripetal force is equal to SUM(Fn) = m V^2/ρ
