AP Physics 1 - unit 5 - torque and rotational motion

kinematics (definition)

the study of motion WITHOUT regards to forces causing it

equations are the same for rotational and linear kinematics

angular displacement VS. linear displacement in rotational kinematics

angular displacement: the change in angle (Δθ)

measured in radians(rad)

linear displacement: the arc length (s)

s=rθ

angular/ rotational velocity VS. linear velocity

angular v: how fast an object is spinning

ω=Δθ/t

linear v: the speed of an object or point tangent to the rotational motion (like a skateboard going forward as a result of the rotation (ω) of the wheels

v=rω

angular/ rotational acceleration VS. linear acceleration

linear	angular
rate of change of tangential velocity as a result of angular α	how fast an object speeds up while spinning, rate of change of angular velocity
a=rα	α=Δω/Δt

torque (τ) (definition, eq, units)

torque: a force that acts to the radius of an object causing acceleration in rotation

τ = F⊥r = Fr(cosθ)

τ = Iα

moment of inertia/ rotational inertia (I)

how difficult it is to change rotational motion

generally, for a single point at a fixed distance from an axis

I = mr²

however formulas for spheres, cylinders, thick rings with 2 radiuses and more will be given

Newton’s 2nd Law for rotation

F=ma

τ=Iα

rigid body

an ideal object where there is no deformation; a solid body with a fixed shape, meaning internal distances ( r ) between points remain constant during motion.

rotational equilibrium

sum of torques acting perpendicular to the radius equals zero

Στ=0