Equation InterpretationTwo Pizza Rolls are on the rotating carousel of a microwave oven. One is at the rim (edge) and the other
is midway between the center and rim. In a certain short time interval Δt, they travel a certain angular displacement and a certain distance (length of arc). Identify and compare these quantities for the two Rolls. Assume constant speed of rotation.
Both the pizza rolls are on two circular paths having different radii because one of them is on the rim and another is near the central axis. Their angular velocity are equal . That means they rotate by same angle in equal period of time. So in Δt they make equal angles at the centre. Hence their angular displacements are equal.
But length of arc made by them in equal interval of time that is Δt are different. Ir is so because their speed are different . Speed v and angular speed ω are related to each other as follows.
v = ω r .
So for objects in motion on circular paths having different radii , v are different even if their ω are same.
length of arc l = v Δt
So length of arc will be proportional to their v which will be proportional to r if their ω are same .
Hence length of arc will be proportional to radius of circular path, ie their distance from the centre .
