Angular Kinematics Exam Review

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Questions and Answers

What is the angular displacement formula expressed mathematically?

$\omega = \frac{\theta}{t}$ (correct)
$\theta = \frac{d}{r}$ (correct)
$v_T = \omega \times r$
$d = \theta \times r$

In angular kinematics, counter-clockwise motion is considered negative.

False (B)

What does the right-hand-thumb rule help determine in angular kinematics?

The direction of angular displacement or angular velocity.

Angular velocity is calculated using the formula ____ = angular displacement/change in time.

ω

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Match the following terms in angular kinematics with their definitions:

Angular distance (φ) = Total rotation angle in radians, degrees, or revolutions Angular displacement (θ) = Change in position of an object from its initial to final angle Tangential velocity (vT) = Linear speed of an object moving along a circular path Radius (r) = Distance from the center of rotation to the point of interest

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Which of the following statements about velocity is true?

Angular velocity is greater for longer radii when tangential velocity is equal. (B), Objects with a shorter radius can achieve a higher angular velocity. (D)

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The unit of force is measured in Pascals.

False (B)

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What formula is used to calculate angular acceleration?

α = (ωf – ωi)/t

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Momentum is the product of mass and ______.

velocity

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Match the types of friction with their descriptions:

Static Friction = Force preventing motion between two stationary objects Kinetic Friction = Force opposing motion between moving objects Rolling Friction = Resistance encountered when an object rolls over a surface Fluid Friction = Resistance experienced by objects moving through a liquid or gas

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Which statement about collisions is correct?

Momentum is conserved in all types of collisions. (B)

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The pressure formula is given by P = Area/Force.

False (B)

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What is the formula for impulse?

Impulse = Ft

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What is torque defined as?

Force multiplied by the distance from the axis of rotation (B)

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The moment of inertia (I) is calculated only by mass and does not take into account the distribution of that mass.

False (B)

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What defines a 3rd class lever?

The force is applied between the axis and the resistance.

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The conservation of angular momentum implies that the total angular momentum of a given system remains constant in the absence of __________.

external torques

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Which factor most significantly affects angular momentum?

Distribution of mass (C)

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Match the levers with their characteristics:

1st Class = Force and Resistance on opposite sides of the axis 2nd Class = Resistance is in the middle 3rd Class = Force is in the middle Levers in general = Consist of Axis, Force, and Resistance

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Mechanical advantage increases as the resistance arm (RA) increases relative to the force arm (FA).

False (B)

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What equation represents the mechanical advantage (MA) of a lever?

MA = FA/RA

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The quantity of angular inertia is quantified as __________.

moment of inertia

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In angular kinetics, which of the following is true about the force arm (FA)?

It is the distance from the axis to the point where the force is applied. (A)

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Which principle states that any body in a fluid will experience a buoyant force equal to the weight of the volume of the fluid it displaces?

Archimedes' principle (D)

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Turbulent flow describes fluid layers that move smoothly and predictably.

False (B)

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What does viscosity refer to in the context of fluid dynamics?

Resistance to flow

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The principle that describes how drag increases with the square of the relative velocity of motion is known as the _______ square law.

theoretical

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Match the types of drag with their descriptions:

Form drag = Affected by the area on which the fluid acts Surface drag = Affects moving objects due to skin friction Wave drag = Only felt in water, increases with faster movement Lift = Acts at right angles to the relative flow

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Which factor does NOT directly affect surface drag?

Density of the fluid (B)

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The center of buoyancy is the point at which buoyant forces act, and it coincides with the center of gravity.

False (B)

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What is the relationship between the duration of force and the velocity of an object?

Increase duration of constant force increases velocity

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The coordination of body segments moving together simultaneously usually aims for ______ or force.

accuracy

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What factor influences the buoyancy of an object in a fluid?

Volume of fluid displaced (C)

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Flashcards

Angular displacement

The angle through which a point on a rotating body moves. Measured in radians (rad), degrees (°), or revolutions (rev).

Angular velocity (ω)

The rate of change of angular displacement. Calculated as angular displacement over time.

Tangential velocity (vT)

The linear velocity of a point on a rotating body. Calculated as angular velocity times the distance from the rotation axis.

Radians

A unit of angular measure. One radian is the angle subtended by an arc equal in length to the radius of the circle.

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Angular vs. Linear Displacement

Angular displacement is the rotation, linear displacement is the movement along a straight line. The farther a point from the axis, the greater the linear displacement for a given angular displacement.

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Centripetal Acceleration

Acceleration towards the center of a circular path.

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Newton's Laws of Motion

Fundamental laws describing the relationship between forces, mass, and motion.

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Momentum

Mass times velocity.

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Conservation of Momentum

Total momentum is constant if no external forces act.

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Impulse

Change in momentum of an object.

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Coefficient of Restitution (e)

Measure of elasticity in a collision (0 ≤ e ≤ 1).

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Friction

Force that opposes motion between surfaces in contact.

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Kinetic Link

The coordination of linked body segments to create force or velocity. It can be simultaneous or sequential.

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Simultaneous Kinetic Link

Body segments move together, usually for accuracy or force.

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Sequential Kinetic Link

Body segments move in sequence to create maximum velocity.

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Laminar Flow

Fluid moving in layers, with layers moving relative to each other.

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Turbulent Flow

Fluid layers are disturbed, creating irregular movement.

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Viscosity

Resistance to flow, or the ease of movement between fluid layers.

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Buoyancy

The tendency of an object to float or rise in a fluid.

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Archimedes' Principle

The buoyant force on an object is equal to the weight of the fluid displaced by the object.

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Form Drag

Drag caused by the shape of an object moving through a fluid.

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Surface Drag

Drag caused by friction between the surface of an object and the fluid it's moving through.

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Torque

The turning effect of a force. Calculated as force multiplied by the perpendicular distance from the force's line of action to the axis of rotation.

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Lever

A simple machine consisting of a rigid bar that pivots around a fixed point called a fulcrum.

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Mechanical Advantage (MA)

A ratio of the force produced by a machine to the force applied to it. A measure of how much a machine multiplies a force.

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Angular Inertia (Ia)

A measure of an object's resistance to changes in its angular velocity.

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Radius of Gyration (k)

The distance from the axis of rotation to the point where the body's mass can be concentrated without changing its angular inertia.

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Moment of Inertia (I)

The quantitative measure of angular inertia (I = mk2).

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Angular Momentum (H)

The product of an object's moment of inertia and its angular velocity (H = Iaω).

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Conservation of Angular Momentum

In the absence of external torques, the total angular momentum of a system remains constant.

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Skill Phasing

Analyzing a skill by identifying different phases, improving each step

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MPA

Method of analyzing and improving motor skills

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Study Notes

Exam 2 Review

This material is a summary of the lecture content for the second exam.
Students need to consult their notes, PowerPoint slides, and textbook readings for better understanding.
Formula sheet will be provided.

Lecture: Angular Kinematics

Relative vs. Absolute Angle: Angular distance (φ) vs. Angular Displacement (θ). Similar to linear, counter-clockwise is positive, clockwise is negative.
Measurements: Degrees, revolutions, and radians. Number of radians = arc length/radius.
Angular Distance vs. Displacement: Greater distance from rotation axis = greater linear displacement.
Angular Velocity (ω): Angular displacement/change in time (ω = θ/t).
Tangential Velocity (v₁): v₁ = ω x r (tangent to arc at a point) perpendicular to the radius at the arc. Longer radius = greater tangential velocity (v₁), for the same angular velocity (ω).
Angular Acceleration (α): α = (ωf - ωi)/t
Centripetal and Centrifugal Acceleration: Centripetal (ac) = v²/r, Centrifugal (af) = mv²/r
Important Concept (Kinetics/Forces): A force is measured in Newtons (N) and is equal to kg⋅m/s².

Lecture: Linear Kinetics (Forces)

Unit of Force: Newton (N) = kg⋅m/s²
Newton's Laws:
- Inertia
- Acceleration
- Action/reaction
Friction:
- Static friction: μs ≤ fs/Fn
- Kinetic friction: μk ≤ fk/Fn
- Rolling friction
Momentum: Mass × velocity. A vector quantity (direction and magnitude).

Lecture: Angular Kinetics

Torque: Torque (τ) = F x d (perpendicular distance of force from axis of rotation).
Levers:
- Axis (fulcrum)
- Force (motive force)
- Resistance (resistance force)
- 1st, 2nd, & 3rd class levers
- Mechanical Advantage (MA) = FA/RA

Important Considerations in Collisions

Conservation of Momentum: Momentum before collision = momentum after collision (no external forces). m₁v₁ (before) + m₂v₂ (before) = m₁v₁ (after) + m₂v₂ (after)
Impulse: Impulse = Ft = m₂v₂ - m₁v₁.
Collisions: Elastic vs. Inelastic.
Elasticity: Measured by Coefficient of Restitution (e). Determined by object composition and surface of the colliding object, and temperature.
Calculation: e = separation speed/approach speed or √(hb/ha) (sqr rt of bounce height/drop height).

Lecture: Angular Momentum & Kinetic Links / MPA

Angular Momentum: Moment of Inertia (I) x Angular Velocity (ω) = H = lω or mk2ω
- Affected by mass and distribution of mass (k) (radius of gyration)
Conservation of Angular Momentum: Total angular momentum remains constant.
- No external torques.
- Changes in angular velocity requires changes of mass distribution (ex. tucking).
MPA (Mechanical Performance Analysis): 3 main steps (Skill phasing, principles/performance factors application, coaching/feedback).
Kinetic Links: Coordination of linked body segments for force/velocity (body segments move together).

Lecture: Fluid Dynamics

Characteristics of Fluid:
- Laminar flow (layers)
- Turbulent flow (disturbed layers).
- Ease of flow = viscosity (resistance).
Buoyancy: Tendency of object to float. Archimedes' principle: buoyant force = weight of displaced fluid.
Drag: Opposing force to object through fluid.
- Form drag (profile).
- Surface drag (skin friction).
Lift: Acts at right angles to relative flow. Pressure differences (high to low).
Magnus Effect: Spin on a ball causes it to curve.

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Questions and Answers

What is the angular displacement formula expressed mathematically?

In angular kinematics, counter-clockwise motion is considered negative.

What does the right-hand-thumb rule help determine in angular kinematics?

Angular velocity is calculated using the formula ____ = angular displacement/change in time.

Match the following terms in angular kinematics with their definitions:

Which of the following statements about velocity is true?

The unit of force is measured in Pascals.

What formula is used to calculate angular acceleration?

Momentum is the product of mass and ______.

Match the types of friction with their descriptions:

Which statement about collisions is correct?

The pressure formula is given by P = Area/Force.

What is the formula for impulse?

What is torque defined as?

The moment of inertia (I) is calculated only by mass and does not take into account the distribution of that mass.

What defines a 3rd class lever?

The conservation of angular momentum implies that the total angular momentum of a given system remains constant in the absence of __________.

Which factor most significantly affects angular momentum?

Match the levers with their characteristics:

Mechanical advantage increases as the resistance arm (RA) increases relative to the force arm (FA).

What equation represents the mechanical advantage (MA) of a lever?

The quantity of angular inertia is quantified as __________.

In angular kinetics, which of the following is true about the force arm (FA)?

Which principle states that any body in a fluid will experience a buoyant force equal to the weight of the volume of the fluid it displaces?

Turbulent flow describes fluid layers that move smoothly and predictably.

What does viscosity refer to in the context of fluid dynamics?

The principle that describes how drag increases with the square of the relative velocity of motion is known as the _______ square law.

Match the types of drag with their descriptions:

Which factor does NOT directly affect surface drag?

The center of buoyancy is the point at which buoyant forces act, and it coincides with the center of gravity.

What is the relationship between the duration of force and the velocity of an object?

The coordination of body segments moving together simultaneously usually aims for ______ or force.

What factor influences the buoyancy of an object in a fluid?

Flashcards

Angular displacement

Angular velocity (ω)

Tangential velocity (vT)

Radians

Angular vs. Linear Displacement

Centripetal Acceleration

Newton's Laws of Motion

Momentum

Conservation of Momentum

Impulse

Coefficient of Restitution (e)

Friction

Kinetic Link

Simultaneous Kinetic Link

Sequential Kinetic Link

Laminar Flow

Turbulent Flow

Viscosity

Buoyancy

Archimedes' Principle

Form Drag

Surface Drag

Torque

Lever

Mechanical Advantage (MA)

Angular Inertia (Ia)

Radius of Gyration (k)

Moment of Inertia (I)

Angular Momentum (H)

Conservation of Angular Momentum

Skill Phasing

MPA

Study Notes

Exam 2 Review

Lecture: Angular Kinematics

Lecture: Linear Kinetics (Forces)

Lecture: Angular Kinetics

Important Considerations in Collisions

Lecture: Angular Momentum & Kinetic Links / MPA

Lecture: Fluid Dynamics

Studying That Suits You

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