Summary Section 1: Further Mechanics

Section 1:
Further Mechanics


Circular Motion

 To convert from degrees to radians: multiply the degree angle by π/180

Angular Speed:

 This is the angle an object rotates through per second

𝛳 (𝑟𝑎𝑑)
𝜔 (𝑟𝑎𝑑 𝑠 −1 ) =
𝑡 (𝑠𝑒𝑐𝑜𝑛𝑑𝑠)

- 𝜔 – Angular speed
- 𝛳 – Angle the object turns through
- 𝑡 – time

Considering that Speed = distance / time:

𝑟𝛳(𝑎𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ)
𝑣=
𝑡

𝑣 (𝑚𝑠 −1 )
𝜔 (𝑟𝑎𝑑 𝑠 −1 ) =
𝑟 (𝑚)

Frequency and period:

 The frequency is the number of complete revolutions that occur in one second (rev s-1)
 The period is the time taken for a complete revolution (in seconds)

1
𝑓=
𝑇

For a complete circle, an object turns 2π radians in time T. So, the equation for angular speed becomes:

2𝜋
𝜔=
𝑇

By combining the two equations, we get:



𝜔 = 2𝜋𝑓