rock.freak667 said:ω=dθ/dt
now θ is the angle of an arc of a circle of radius r and arc length l.
so θ=l/r
So ω=d/dt(l/r)
r doesn't change so
rω=dl/dt
and dl/dt=v
so rω=v
emyt said:Hi, thanks a lot for the reply. Do we say θ=l/r because the arc length might not be in radians?
thanks
rock.freak667 said:Are length is defined as l=rθ when θ is in radians.
dθ/dt is the derivative of θ with respect to time. In other words, it represents the rate of change of the angular displacement, or how quickly the angle is changing over time.
v/r is the ratio of the linear velocity (v) to the radial distance (r). It is used to calculate the angular velocity, or how quickly an object is rotating around a fixed point.
The relationship between dθ/dt and v/r is that they both represent rates of change. dθ/dt measures the change in angular displacement over time, while v/r measures the change in linear velocity over a specific radial distance. They are related by the formula dθ/dt = v/r, where v is the linear velocity and r is the radial distance.
Exploring this relationship is important because it helps us understand the motion of rotating objects. By studying the rates of change of angular displacement and linear velocity, we can better understand how objects move and predict their future positions. This relationship is also crucial in many fields such as physics, engineering, and astronomy.
Yes, the relationship between dθ/dt and v/r can be applied to any type of motion, not just circular motion. As long as there is a fixed point and a change in angular displacement and linear velocity, this relationship can be used to analyze and understand the motion of an object.