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
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
