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.

<p>ω</p> Signup and view all the answers

Match the following terms in angular kinematics with their definitions:

<p>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</p> Signup and view all the answers

Which of the following statements about velocity is true?

<p>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)</p> Signup and view all the answers

The unit of force is measured in Pascals.

<p>False (B)</p> Signup and view all the answers

What formula is used to calculate angular acceleration?

<p>α = (ωf – ωi)/t</p> Signup and view all the answers

Momentum is the product of mass and ______.

<p>velocity</p> Signup and view all the answers

Match the types of friction with their descriptions:

<p>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</p> Signup and view all the answers

Which statement about collisions is correct?

<p>Momentum is conserved in all types of collisions. (B)</p> Signup and view all the answers

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

<p>False (B)</p> Signup and view all the answers

What is the formula for impulse?

<p>Impulse = Ft</p> Signup and view all the answers

What is torque defined as?

<p>Force multiplied by the distance from the axis of rotation (B)</p> Signup and view all the answers

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

<p>False (B)</p> Signup and view all the answers

What defines a 3rd class lever?

<p>The force is applied between the axis and the resistance.</p> Signup and view all the answers

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

<p>external torques</p> Signup and view all the answers

Which factor most significantly affects angular momentum?

<p>Distribution of mass (C)</p> Signup and view all the answers

Match the levers with their characteristics:

<p>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</p> Signup and view all the answers

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

<p>False (B)</p> Signup and view all the answers

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

<p>MA = FA/RA</p> Signup and view all the answers

The quantity of angular inertia is quantified as __________.

<p>moment of inertia</p> Signup and view all the answers

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

<p>It is the distance from the axis to the point where the force is applied. (A)</p> Signup and view all the answers

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?

<p>Archimedes' principle (D)</p> Signup and view all the answers

Turbulent flow describes fluid layers that move smoothly and predictably.

<p>False (B)</p> Signup and view all the answers

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

<p>Resistance to flow</p> Signup and view all the answers

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

<p>theoretical</p> Signup and view all the answers

Match the types of drag with their descriptions:

<p>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</p> Signup and view all the answers

Which factor does NOT directly affect surface drag?

<p>Density of the fluid (B)</p> Signup and view all the answers

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

<p>False (B)</p> Signup and view all the answers

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

<p>Increase duration of constant force increases velocity</p> Signup and view all the answers

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

<p>accuracy</p> Signup and view all the answers

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

<p>Volume of fluid displaced (C)</p> Signup and view all the answers

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).
  • 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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