The thesis is divided in three parts based largely on published articles or on manuscripts submitted for publication. First we propose a new method which is called the shooting-bead method. This method is a fast and easy experimental technique for evaluating cantilever stiffness and flexural rigidity of semi-flexible to semi-rigid rod-like biological and nano-filaments based on the measurement of just two distances. The method is based on applying a force normal to the filament with a microsphere bead trapped in the laser tweezer followed by its sudden release. Through a simple measurement of the distances that the bead moves, the flexural rigidity of the filament can be found from the formula derived in this paper. Then we take into account the effects of the viscous drag force exerted on the filament itself. To this end, we have defined a key variable, called the filament energy-loss factor (or filament drag factor) that accounts for all the energy-loss effects. It has been shown that the effect due to the consideration of filament energy-loss factor on calculation of the flexural rigidity increases with increasing the flexibility of the filament. Finally, in the third part we discuss the effect of ultrasound on the microtubules. Here we have analytically solved equations of motion for the vibrational dynamics of an MT that is attached at its two ends. This is especially relevant for MTs during mitosis when they attach to chromosomes and centrosomes. Our analysis applies to MTs present inside a viscous solution and when driven by an ultrasound plane wave. We have shown that with using ultrasound plane waves the resonance condition for the MT treated as a rigid rod cannot be provided, and in order to achieve resonance we should excite a single mode of the MT with a harmonic number larger than a threshold value introduced in this thesis. Single mode excitation not only helps to transfer the minimum amount of energy to the surrounding medium compared with multi-mode excitation but it also allows for a simultaneous high-amplitude and high-quality factor which is impossible when using plane waves.

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Light vehicle rollover accidents on soft surfaces can be modeled assuming constant drag with linear motion equations and other engineering principles. The concept of using segment average results to evaluate roll mechanics parameters throughout a roll sequence, and specifically, segment duration to evaluate vehicle trajectory between ground impacts is developed. The trajectory model is presented, explained and compared to values obtained by analyzing digital video of rollover crash tests. Detailed film analysis procedures are developed to obtain data from rollover crash tests that are not otherwise documented. Elevation of the center of gravity of vehicles is obtained where instrumentation does not explicitly yield this data. Instantaneous center of gravity elevation data throughout a roll sequence provides the opportunity to calculate descend distances as a vehicle travels from one ground contact to another. This data is used to quantify severity of ground impacts as a vehicle interact with the ground throughout a roll sequence. Segment average analysis is a reasonable method for determining general roll mechanics parameters. Because of the chaotic nature of rollover accidents, the range of effective drag factors for a given roll surface may be quite large. Choosing an average of typical drag factors is a reasonable approach for a first-order approximation although certain parameters may be predicted less accurately than if actual values were known. The trajectory results demonstrate the influence of drag factor descent height calculations. Typical constant drag factors tend to overestimate descent height early in a roll sequence and underestimate descent height later in the sequence. The trajectory model is a useful tool to aid in understanding rollover mechanics although a rolling vehicle may be in contact with the ground for a significant fraction of a roll segment. The model should not be used at locations in roll sequences where there are extremes in translational center of gravity decelerations. These extremes include the segments immediately following overturn where there are large angular accelerations and large differences between the tangential velocity of the vehicle perimeter and the translational velocity of the center of gravity, as well as segments that include vehicle impacts with irregular topography.