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A2L Item 018

Meta-Information
Description: 
Identify the direction of acceleration when traveling in a vertical circle.
Goal: 
Honing the concept of acceleration especially regarding circular motion.
Level: 
High School
Keywords: 
Acceleration
Keywords: 
Mechanics
Keywords: 
Rotational 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

Answer

(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?