Dynamics and Stability – Exercises Module 1: Newton’s Laws and Fictitious Forces

Course week(s) 1. Newton’s Laws and Fictitious Forces

Corresponding to each module, as described in the lectures section, the teachers handed out one or more sample problems. These are worked out examples that illustrate how to work with a certain method.

Next to the given sample problems, several recommended exercises are given. These exercises can be found in the textbook of this course (Analytical Mechanics, by Josef S. Tőrők). More on this textbook can be found in the readings section.

Sample problems:

Foucault’s pendulum The first sample problem is about the Foucault’s pendulum. This pendulum is the first device that proved the rotation of the earth and makes use of the fictitious forces discussed in the lecture slides.

Kinetic energy of helicopter rotor The second sample problem deals with the rotors of a helicopter. The kinetic energy of the rotor is analyzed. This sample problem serves as an introduction to Module 2, where the energy principle is further elaborated.

Recommended exercises:

Solve the exercises in the provided order:

1.147 (Choose the x-axis coinciding with the longitudinal axis of the airplane, the z-axis pointing upward and the propeller blade coinciding with the y-axis for t=0. Be careful with the units!)
1.190
4.40
1.112
1.158
1.169 (Colatitude is the complementary angle to the latitude)
4.14(b)
4.41
1.207

Answers exercises This file contains answers and hints corresponding to the following recommended exercises of this module: 1.112, 1.147, 1.158, 1.169, 1.190, 1.207, 4.14(b), 4.40, 4.41.

Elaboration exercises This file contains elaboration of the following exercises: 1.167, 1.169, 1.170, 1.207, 4.40.

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