http://www.ck12.org Chapter 9. Rotational Motion
- Imagine spinning a fairly heavy disk. To make it spin, you don’t pushtowardsthe disk center–that will
just move it in a straight line. To spin it, you need to push along the side, much like when you spin a
basketball. Thus, thetorqueyou exert on a disk to make it accelerate depends only on the component of the
force perpendicular to the radius of rotation:τ=r F⊥. - Many separate torques can be applied to an object. The angular acceleration produced isα=τnet/I.
- When an object is rolling without slipping this means thatv=rωanda=rα. This is also true in the situation
of a rope on a pulley that is rotating the pulley without slipping. Using this correspondence between linear
and angular speed and acceleration is very useful for solving problems, but is only true if there is no slipping.
MEDIA
Click image to the left for more content.- Theangular momentumof a spinning object isL=Iω. Torques produce a change in angular momentum with
time:τ= 4 L/ 4 t
MEDIA
Click image to the left for more content.- Spinning objects have a kinetic energy, given byK= 1 / 2 Iω^2.
Analogies Between Linear and Rotational Motion
Linear
Quantity Units
x m
v m/s
m kg
F=∆∆pt N
a=FNetm m/s^2
p=mv kg m/s
K=^12 mv^2 JRotational
Quantity Units
θ Radians
ω Radians/s
I kg m^2
τ=∆∆Lt N m
α=τNetI Radians/s^2
L=Iω kg m^2 /s
K=^12 Iω^2 J