S5.1 Linear and rotational motion

[A] Analogies between linear and rotational motion

To describe rotational motion we use angular variables. These are defined so that Newton’s laws take on their familiar forms when expressed in angular form. The rotational analogues of linear variables and physical laws are listed below.

Key Point 5.1

Linear MotionAngular Motion
positionxθangle
velocity$\vec{v}$$\vec{\omega}$angular velocity
acceleration$\vec{a}$$\vec{\alpha}$angular acceleration
massmImoment of inertia
momentum$\vec{p}$$\vec{L}$angular momentum
force$\vec{F}$$\vec{\tau}$torque
$\vec{F}=m \vec{a}$$\vec{\tau}=I\vec{\alpha}$
$\vec{p}=m\vec{v}$$\vec{L}=I \vec{\omega}$
K.E.$K=\frac{1}{2}m v^2$$K_R = \frac{1}{2} I \omega^2$Rotational K.E.

These equations are more than a convenient rewriting of Newton’s laws. They contain new physics, in particular the law of conservation of angular momentum. During this module, we will explore these analogues, and their consequences.

Be warned: they can be very counterintuitive!