Test #2 - Mechanical Analysis

A collection of 80 flashcards covering key concepts and definitions related to linear kinematics in two dimensions, designed to aid in exam preparation.

What is the apex in projectile motion?

The highest point of a projectile's trajectory.

What are the components of a vector?

Parts of a resultant vector, typically represented as the x and y components.

Define net value in kinematics.

The total vector quantity, represented as the resultant.

What is a parabola in the context of motion?

The airborne path of a projectile, typically U-shaped.

What does 'plane' refer to in kinematics?

A flat, two-dimensional surface defined by two axes.

Define a projectile.

An object that is thrown or propelled into the air, subject only to gravitational force and air resistance after leaving the ground.

What is meant by the range of a projectile?

The horizontal distance a projectile travels.

What is relative height?

The difference in height between the take-off position and landing position.

What is a resultant vector?

A single vector that has the same effect as two or more vectors combined.

What is a trajectory?

The path followed by a projectile.

What needs to be defined when describing a frame of reference?

A plane where motion refers to planar motion.

How is motion defined in a plane?

Motion within a smooth flat space defined by two axes.

What is the average velocity of the kick returner described in the example?

8 yards/sec.

Why did the football run take longer than expected?

It took him 14.18 seconds instead of the estimated 12.5 seconds.

What is the definition of a resultant in vector analysis?

A vector that combines the effects of two or more vectors.

What are x and y components in vectors?

Parts of a resultant vector acting in different directions: X components are horizontal, Y components are vertical.

How do you calculate the resultant velocity from components?

Use the formula R = sqrt(Rx^2 + Ry^2).

What are the x and y dimensions in the football field example?

X direction: 100 yards, Y direction: 53.5 yards.

What trigonometric formula is used for resultant velocity calculation?

R = sqrt(Rx^2 + Ry^2).

What is the result of calculating the resultant velocity of the example?

113.4 yards.

What is the formula to calculate time based on resultant velocity?

t = distance/velocity.

What are the key definitions of basic trigonometric functions?

Sin(θ) = opposite/hypotenuse, Cos(θ) = adjacent/hypotenuse, Tan(θ) = opposite/adjacent.

What is the maximum height in a projectile jump?

Maximum vertical position before descent begins.

How is correction factor used when vectors don't align with an axis?

Apply sine and cosine functions for respective sides.

What does a correction factor apply to?

It applies when a vector does not align with an axis.

What happens to components at a 45-degree angle?

The magnitudes of x and y components are equal.

What is gravity's effect on projectile motion?

Gravity acts downwards and is a constant force.

What is the acceleration due to gravity?

-9.81 m/s² or -32 ft/s².

What equation represents velocity and displacement in constant acceleration?

Δp = vi * t + (1/2) * a * t^2.

How is final velocity calculated?

vf = vi + at.

What is an example of calculating resultant velocity with an angle?

Resultant velocity of 18 m/s at an angle of 35 degrees.

What is the formula for calculating moment of inertia for a point mass?

I = mr^2.

What defines angular position?

Orientation of a rigid body relative to an axis, measured in degrees or radians.

What is angular velocity?

Rate of change of angular position over time.

How do you measure angular acceleration?

By the formula α = Δω / Δt.

What defines linear momentum?

Resistance to change in velocity of a moving body.

What is the formula for linear momentum?

L = mv, where L is momentum, m is mass, and v is velocity.

Explain the concept of inertia.

A tendency to change in motion, specifically a resistance to change in a body’s velocity.

How is weight calculated?

Weight (W) is calculated using W = mg, where g is acceleration due to gravity.

What is the relationship between mass and inertia?

Mass is a measure of inertia; more mass means greater resistance to changes in motion.

What is linear inertia?

It refers to the resistance to change in a body’s linear motion.

What is the equation for center of mass?

It refers to the geometrical point where all mass is considered to be connected.

Define moment of inertia for a rigid body.

It is the sum of individual moments of inertia: I = sum(mr²).

What is the relationship between angular momentum and moment of inertia?

H = I * ω, where H is angular momentum, I is moment of inertia, and ω is angular velocity.

What is a significant consideration for altering performance in jumping?

Adjusting the release angle can maximize range and height.

What is an effective way to measure performance improvements?

By investigating change in thrust and trajectory characteristics.

What impacts the performance of elderly individuals during movement?

Changes in inertia and momentum can affect their balance and control.

How can angular velocity affect linear speed?

A larger wheel diameter can yield a higher linear speed at the same angular velocity.

What is the importance of analyzing jumping mechanics?

It provides insights for improving athletic performance and safety measures.

What is the Pythagorean theorem used for in kinematics?

To calculate the resultant from vertical and horizontal components.

What does a higher angle of takeoff imply for projectile motion?

Generally results in a greater maximum height at the expense of range.

What is the effect of time of flight on projectile performance?

It determines how long the object stays airborne, affecting overall distance.

What are the key results summarized in projectile motion equations?

Velocity, angle of takeoff, resultant velocity, and moment of inertia are all essential.

Define relative height in relation to projectile motion.

It is the difference in heights between the launch and landing points of a projectile.

How does angular acceleration differ from linear acceleration?

Angular acceleration refers to changes in angular velocity, while linear acceleration pertains to linear velocity.

What variables determine the trajectory of a projectile?

Initial velocity, release angle, and acceleration due to gravity.

How does corrective feedback improve jump performance?

It helps identify the most effective adjustments to optimize takeoff angles.

if the moment of inertia of a bat increases, is the bat harder or easier to swing?

harder

linear momentum is the product of what two variables?

mass and linear velocity

angular momentum is the product of what two variables?

moment of inertia and angular velocity

weight is the product of which two variables?

mass and acceleration due to gravity

which variable has the greatest influence on moment of inertia?

radius of gyration and mass

when examining angular velocity, the velocity vector will always be ______ to the rigid body

perpendicular

rotation in the clockwise direction is considered to be ______.

negative

if both angular velocity and angular acceleration are positive, what is happening to the magnitude of the angular velocity vector?

it is increasing in the positive direction

if angular velocity is negative and angular acceleration is positive, what is happening to the magnitude of the angular velocity vector?

it is decreasing in the negative direction

if a person jumps at an angle of 35 degrees CCW from the ground, which of the following statements is true?

the x component of velocity is greater than the y component of velocity

what kinematic term describes how fast a segment is rotating in a particular direction?

angular velocity

what kinematic term describes how quickly or slowly a segment is changing its rate of rotation in a specific direction?

angular acceleration

what term accounts for the change in the magnitude of the linear velocity vector?

tangenital acceleration

what term accounts for the change in the direction of the linear velocity vector?

centripetal acceleration

initial x velocity

cos

initial y velocity

sin

total time

Vf - Vi / a

range

Vx(t)

height

-Vy² / 2 a

x component of velocity

range/time

y component of velocity

*divide time in half

(a)(t)

resultant

(unit square) Vx² + Vy²

angle of takeoff

tan^-1 Vy/Vx

angular displacement

0f - 0i

angular velocity

0f-0i/t

angular acceleration

wf - wi/ t

linear velocity

v = rw (57.3)

linear momentum

(m)(v)

weight

(m)(g)

moment of inertia/radius of gyration

I = mk²

angular momentum

H = (I) (w)

point of mass

I = mr²