Circular Motion
Although the natural state of motion for a body is to move in a straight line, particles can be made to move in a uniform circle as well.
When a particle moves in a circle, it has both linear velocity and angular velocity.
Linear velocity is usually represented by "V"
Angular velocity is represented by the lower case greek letter omega "ω"
We know how to define linear velocity, it's the distance travelled per unit time. Angular velocity is defined in a similar way.
Suppose a particle moves around a circle of radius, r at a constant angular velocity, ω.
Although the natural state of motion for a body is to move in a straight line, particles can be made to move in a uniform circle as well.
When a particle moves in a circle, it has both linear velocity and angular velocity.
Linear velocity is usually represented by "V"
Angular velocity is represented by the lower case greek letter omega "ω"
We know how to define linear velocity, it's the distance travelled per unit time. Angular velocity is defined in a similar way.
Suppose a particle moves around a circle of radius, r at a constant angular velocity, ω.
If the particle is initially at a point P, and then turns through an angle, θ (In radians) to a point Q, travelling a distance of S in a time t...
We can define the angular velocity, ω=θ/t, however ; S=rθ ===> θ=S/r
∴ω=S/tr
We now have that ω=S/tr. But we know that the linear velocity v = distance/time
=s/t
∴ω=v/r
The angular velocity can be thought of as the rate of change of the angle with respect to time.
So in calculus terms ,
ω=dθ/dt
If our particle is moving with a uniform angular velocity, we can also find the time period T, the time it takes to go round in a full circle once.
For the particle to go round in a full circle, the angle it would need to turn through is 2π radians. If it turns through ω radians per second, then
T=2π/ω
As for acceleration, defining the angular acceleration is easy, it's the rate of change of the angular velocity
If a particle goes from angular velocity
We can define the angular velocity, ω=θ/t, however ; S=rθ ===> θ=S/r
∴ω=S/tr
We now have that ω=S/tr. But we know that the linear velocity v = distance/time
=s/t
∴ω=v/r
The angular velocity can be thought of as the rate of change of the angle with respect to time.
So in calculus terms ,
ω=dθ/dt
If our particle is moving with a uniform angular velocity, we can also find the time period T, the time it takes to go round in a full circle once.
For the particle to go round in a full circle, the angle it would need to turn through is 2π radians. If it turns through ω radians per second, then
T=2π/ω
As for acceleration, defining the angular acceleration is easy, it's the rate of change of the angular velocity
If a particle goes from angular velocity