Physics 4A - Chapter 11

Rolling Without Slipping: d_cm (distance travelled by center of mass) = …

s = rθ

Rolling Without Slipping: v_cm = …

rω

Rolling Without Slipping: a_cm = …

rα

Conservation of Mechanical Energy in Rolling Motion: Eτ = …

$$\frac12mv^2+\frac12I\omega^2+mgh$$

Conservation of Mechanical Energy in Rolling Motion

E_i = E_f

‘cause its conserved (i cant believe i had to remind myself of this)

Angular Momentum of a Particle: L (angular momentum of particle) = …

r x p, where p is the particles linear momentum

Relationship Between Torque and Angular Momentum

$\frac{d\overrightarrow{I}}{dt}=\Sigma\tau$ (L not I oops)

Total Angular Momentum Formula

$$\overrightarrow{L}=\overrightarrow{I}\left(1\right)+\overrightarrow{I}\left(2\right)+\cdots+\overrightarrow{I}\left(n\right)$$

Total Angular Momentum and Torque Relation

$$\frac{d\overrightarrow{L}}{dt}=\Sigma\overrightarrow{\tau}$$

Conservation of Angular Momentum

$\overrightarrow{L}=\overrightarrow{I}\left(1\right)+\overrightarrow{I}\left(2\right)+\cdots+\overrightarrow{I}\left(n\right)$ = constant

or

$\frac{d\overrightarrow{L}}{dt}$ = 0

then L = Iω, where this equation is analogous to the magnitude of linear momentum, p = mv

Conservation of Angular Momentum in Regard to L

L_i = L_f

Conservation of Mechanical Energy in Rolling Motion Continued:

mgh = (1/2)mv² + (1/2)Iw²