Ch 7 Rotational Motion


Check out HyperPhysics Rotational Motion

The concept map below (click to link to the site) from Hyperphysics shows the connections to many important ideas in rotational motion.
Each of the ideas have examples and clear explanations including well laid out math solutions.

rotational_Motion_HYPERhysics.gif


Centripetal Force

This circular motion topic is common to both the college curriculum and Regents physics. Linear units ONLY for the Regents! Angular units and linear units
for the college curriculum.

Centripetal force and centripetal acceleration vectors BOTH point to the center of the circular motion. The velocity vector is pointed along the line tangent to
the curve at any instant. The challenge for many students is to imagine that there is an acceleration produced when speed is constant. REMEMBER that a
vector has both direction and magnitude so a change in the direction of the velocity vector is what produces the acceleration. Imagine the tangent constantly
pointing different directions as an object completes a circular path.
centacc.gif
FsubCformula.gif
centripetal_vector-diagram.png
Looking down on a mass connected to a string.
Once the string is cut, the mass moves off in a
straight line going to direction of the velocity vector
at the point the string was cut.
cutrope.gif
http://regentsprep.org/regents/physics/phys06/bcentrif/default.htm

Angular Motion Formulas

Concept............

Linear Formula..........
Angular Formula..........
Angular Variables
Displacement

d = vi t + 1/2 a t ^2
θ = ωo t + 1/2 α t ^2
θ = angular displacement (rad)
ωo = angular velocity at time zero (rad/s)
α = angular acceleration (rad/s2)
Velocity

v = d / t

vf = vi + at

vf ^ 2 = vi ^ 2 + 2ad
ω = θ / t

ω = ωo + α t

ωf ^ 2 = ωo^ 2 + 2 α θ
ω= angular velocity (rad/s)
θ = angular displacement (rad)
t = time (s)
Acceleration

a = (vf - vi) / t
α = (ωf - ωo) / t
ωf = angular velocity at final time (rad/s)
ωo = angular velocity at time zero (rad/s)
α = angular acceleration (rad/s2)
Displacement

d = r θ
θ = d / r

Velocity

v = r ω
ω = v / r

Acceleration

a = r α
α = a / r