Question

Hummingbirds may seem fragile, but their wings are capable of sustaining very large forces and accelerations. (Figure 1) shows data for the vertical position of the wing tip of a rufous hummingbird.

What is the maximum acceleration of the wing tips, in m/s²?

What is the maximum acceleration of the wing tips, in units of g?

Answer 1

Concepts and reason

The required concepts to solve the problem are angular velocity and angular acceleration.

First, from the given time period and position graph, find the angular velocity and thus find the angular acceleration. Then, find the angular acceleration in terms of.

Fundamentals

Angular velocity is defied as the rate of change of angular position of a body that is rotating. The relation between the period of rotation and angular velocity is,

Here, is the time period.

The maximum acceleration is the rate of change of angular velocity.

Here, is the distance or amplitude.

The equation connecting time period and angular velocity is,

Substitute for .

The acceleration is,

Substitute for and for .

The angular acceleration in m/s² is,

Dividing the acceleration with acceleration due to gravity, ,

Ans:

The acceleration of the wing tips is .

The acceleration of the wing tips is .