Question

Bart and Lisa are sitting on a merry-go-round of a certain radius. Bart sits halfway out from the center of the merry-go-round while Lisa sits right on the edge. The merry-go-round is then set in motion, completing a constant number of revolutions each minute.

Which of the following must be the same for both children?

Answer 1

Here as shown in the figure,we have the Bart is sitting at the halg of the radius(at point B) from the centre O and the Lisa is sitting at the edge of the merry go round(at point A) at a distane equal to radius from the centre of the circle.

Location of Lisa from centre,

Location of Lisa from centre,

So,We have if the merry go round is rotating at an angular velocity of about its centre O,

The angular velocity for all the points in the merry go round are equal,which doesnot depends on the distance form the axis of rotation or centre to the point.

But the tangential velocity at a point of distance from centre is,

Consequently linear acceleration is also different for both since it too depends on distance from centre or on the linear velocity.

So,The tengential velocity at any point is depend on the distance to the point from axis of rotation or centre.

So,Since the distance from the axis of rotation or centre to the locations of sitting of Lisa and Bart are different,So,Thier tangential or linear velocity are diofferent,but thier angular velocity of rotation are same.(Which is same for all the poins in merry go round).

So,The angular velocity is same for both Lisa and Bart.