Скачать или смотреть Formula Summary - Bridge equations between angular and linear entities

Distance travelled along a circle, linear velocity, tangential and centripetal acceleration, and torque.

Distance Traveled Along a Circle:
Distance = 𝜃 ⋅𝑅

θ is the angular displacement and
R is the radius.

Linear Velocity:
v=ω×r

ω is the angular velocity and
r is the position vector r

Tangential Acceleration:
𝑎 =α⋅R

α is the angular acceleration.

Centripetal Acceleration:
𝑎 = v^2/R
v is the linear velocity.

Torque:
τ=r×F
where
r is the vector from the pivot to the location of the force and F is the force.

Rotational Inertia:
𝐼 =∑m r^2

m is the mass of each particle and
r is the distance of the particle from the axis of rotation.

These equations link angular quantities with their linear counterparts and describe the motion and forces in rotational dynamics.