Rotational & Linear

Kinematics



Kinematics Concepts:

Concept

Linear

Rotational/Angular

Position

x
theta

Displacement

delta x = x - x_sub_o
delta theta = theta - theta_sub_o

Average Velocity

v_bar = delta x/delta t
omega_bar = delta theta/delta t

Instantaneous Velocity

v = lim(v_bar) = lim(delta x/delta t) = dx/dt
omega = lim(omega_bar) = etc.

Average Acceleration

a_bar = delta_v/delta_t
alpha_bar = delta omega/delta t

Instantaneous Acceleration

a = lim(a_bar) etc.
alpha = lim(alpha_bar) etc.

Conversions:

x = r theta
v = r omega
a = r alpha


Kinematics of Constant Acceleration:

Linear

Rotational/Angular

v = v_sub_o + at
omega = etc.
delta_x = etc.
delta_omega = etc.
v_bar = etc.
omega_bar = etc.
delta_x = etc.
delta_omega_bar = etc.
v_squared = etc.
omega_squared = etc.


Two Accelerations:

tangential and centripetal accelerationsYou should realize that the acceleration mentioned above (a = r alpha) is a tangential acceleration, which gives the rate at which the rotational velocity changes. A point on a rotating object also has a centripetal, or radial, acceleration which points toward the center of the circle.




last update February 12, 2003 by JL Stanbrough