1. Motion in a circle Flashcards
What is a radian?
The angle subtended at the centre by an arc equal in length to the radius of the circle
How do you convert from degrees to radians?
° * π/180
How do you convert from radians to degrees?
° * 180/π
Define angular displacement (Δθ):
The change in angle, in radians, of a body as it rotates around a circle
Define angular speed:
The rate of change in angular displacement with respect to time
What is the velocity of an object travelling in a uniform circular motion?
The object as constantly changed velocity because it is constantly changing direction and is therefore accelerating
How do you calculate angular speed (⍵, rad s-1)?
- ⍵ = Δθ/Δt
- ⍵ = 2π/T
- ⍵ = 2πf
- ⍵ = v/r
Define a centripetal force:
The resultant force towards the centre of the circle required to keep a body in uniform motion
In what direction does a centripetal force act?
It is always directed towards the centre of the body’s rotation
In what direction does centripetal acceleration act?
It acts towards the centre of the circle in the same direction as the centripetal force
How does angular speed differ from linear speed?
Angular speed does not change with radius, but linear speed does
Define centripetal acceleration:
The acceleration of an object towards the centre of a circle when an object is in motion rotating around a circle at a constant speed
How do you calculate centripetal acceleration (α, rad s^-2)?
- α = v^2/r
- α = r⍵ ^2
- α = Δ⍵/t
How do you calculate centripetal force?
- F = mv^2/r
- F = mr⍵^2
- F = mca
How do you calculate linear speed?
- v = 2πr/T
- v = ⍵r
