# A2L Item 018

Goal: Honing the concept of acceleration especially regarding circular motion.

Source: UMPERG

A child is swinging. What is the direction of her acceleration when the
swing is at its lowest point?

1. Up
2. Down
3. In the direction of the child’s motion
4. Opposite the direction of the child’s motion
5. Zero acceleration, direction can’t be defined.
6. None of the above
7. Cannot be determined

### Commentary:

(1) The acceleration is in the upward direction. The child is traveling
in a circle and at the lowest point the acceleration is all radial.

#### Background

Circular motion must have been covered for the item to be of use. The
question may be answered using either kinematics or dynamics. The
direction of the acceleration can be realized using kinematics by
drawing the velocity vector just before the lowest point and just after
the lowest point. The difference is proportional to the acceleration
and this difference points toward the center of the circle. At the
lowest point all forces are vertical so the acceleration must also be in
the vertical direction. The tension is larger than the weight so the
acceleration is in the upward direction.

#### Questions to Reveal Student Reasoning

What is the definition of acceleration? What is the direction of the
velocity of the child when at the lowest point of the swing? Is it
getting larger or smaller? Is it changing direction? What forces act
on the child at the lowest point of the swing and in what direction are
these forces?

#### Suggestions

Have students draw a motion plot indicating the position and the
velocity vector of the child at various points in the child’s motion.
Do their drawings reflect that the velocity is always tangent to the
circular path, but increasing in magnitude as the child swings toward
the lowest point?