Question

Four children are playing in a field The children form a line, holding hands The player at the front of the line starts to spin around faster and faster, causing the others to run around her in a circle, as shown in (Figure 1). While the line of children is rotating, which of the following statements are correct? The player at the front of the line has the smallest angular acceleration. The player at the front of the line has the smallest linear velocity. All the children have the same angular acceleration All the children have the same linear velocity.

Answer 1

a) Since they are forming a line, all the children have the same angular velocity and angular acceleration. This expression is FALSE.

b) The linear veloctiy can be calculated like this:

$v=\omega \cdot r$

Where v is the linear velocity, w is the angular velocity and r is the distance from the center to each child. As we can see, the first child (the smallest distance) has the smallest linear velocity while the the last one has the highest linear velocity. This statement is TRUE.

c) As we mentioned before, they are forming a line, so the angular acceleration is the same for all the children. This statement is TRUE.

d) As in B, if the angular velocity is constant (which is true for this problem), the linear velocity depends on the distance from the center to the where the child is. Each child has a different distance, therefore each child has different linear velocity. This expression is FALSE.