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 Motion | Angular Motion | |||
position | x | ↔ | θ | angle |
velocity | ![]() | ↔ | ![]() | angular velocity |
acceleration | ![]() | ↔ | ![]() | angular acceleration |
mass | m | ↔ | I | moment of inertia |
momentum | ![]() | ↔ | ![]() | angular momentum |
force | ![]() | ↔ | ![]() | torque |
![]() | ↔ | ![]() | ||
![]() | ↔ | ![]() | ||
K.E. | ![]() | ↔ | ![]() | 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!