Angular Motion
Angle of displacement is measured in radians or degrees where 360° = 2π rad.
Newton's Second Law tells us that a force acting on a still object causes it to accelerate in the direction of the force. Here, gravity is the force pulling the heavier object down, which, together with friction, causes the angular motion of the pulley.
Test it out
Tap the diagram for more information and click on the buttons to change a component and see what happens!
 Increase $m_2$ Weight Show a Wheel
Example calculations
In order to work with Angular Motion, mechanical engineers need to understand and work with a variety of calculations. Here are just a few:
Angular Displacement ($\theta$):
$\theta = \frac{S}{r}$
$\theta = \omega t + \frac{1}{2} \alpha t^2$
Angular Velocity ($\omega$):
$\omega = \frac{\theta}{t}$
$\omega = 2 \pi f$
Angular Acceleration ($\alpha$):
$\alpha = \frac{\omega}{t}$
 Angle of Displacement $\theta$ Arc Length $S$ Radius $r$ Angular Velocity $\omega$ Angular Acceleration $\alpha$ Time $t$
Angular motion can be defined as the motion, or movement, of an object around a fixed point or axis. In other words, the way an item swings around when one point of it is locked into position. Examples of this are pendulums, wheels, motors, food processors, merry-go-rounds, and even the Earth moving around the sun.
In real life application, this idea also comes into play when you consider loosening or tightening bolts, or closing a valve at a factory. In these cases, you also have an object moving around a fixed point.
When working with angular motion, some key concepts to think about are angular displacement, velocity and acceleration. Each of these is used to talk about a different part of the angular motion picture.
Angular displacement is used to describe the angle an object has moved through from start to finish. Imagine if you were to draw a line following the position of a point from the start, to the end of its journey as it moves. You'd be able to see a circular, or curved line, and measure this angle. Angular velocity measures how quickly the angular displacement happens, and angular acceleration looks at how that velocity changes from start to finish.
To complete the picture, torque refers to how much force you need to change the angular acceleration, while power is the work done. Both of these are factors when looking at topics such as vehicle acceleration, or braking.
Practice Questions
$\omega = 2 \pi f$