Centripetal and Centrifugal Forces
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Questions and Answers

What is the external force applied to a body moving along a curved path with uniform linear velocity called?

  • Centrifugal force
  • Active force (correct)
  • Reactive force
  • Tangential force

    • What is the centrifugal force that acts on a body moving with uniform linear velocity along a circular path known as?

  • Reactive force (correct)
  • Active force
  • Centripetal force
  • Tangential force

    • Which rule can be used to represent angular acceleration through a vector diagram?

  • Left hand rule
  • Fleming's rule
  • Screw rule (correct)
  • Right hand rule

    • What does the vector xx' represent in the context of angular velocity change over time dt?

    <p>Change in acceleration</p> Signup and view all the answers

    What is the name of the axis about which a disc is spinning in the context described?

    <p>Axis of spin</p> Signup and view all the answers

    What is the action of the reactive or centrifugal force on a body moving with uniform linear velocity along a circular path?

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

    What is the mass moment of inertia of the rotor?

    <p>2880 kg-m^2</p> Signup and view all the answers

    What is the angular velocity of precession?

    <p>0.37 rad/s</p> Signup and view all the answers

    What is the gyroscopic couple obtained in kN-m?

    <p>200.866 kN-m</p> Signup and view all the answers

    In which direction does the reactive gyroscopic couple effect cause the ship to move?

    <p>Raise the bow, lower the stern</p> Signup and view all the answers

    Where are gyroscopes commonly used for inertial navigation systems?

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

    What is the effect of the active gyroscopic couple on an airplane during a left-hand turn?

    <p>Raises the nose and dips the tail</p> Signup and view all the answers

    In a naval ship, what is the fore end called?

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

    What happens to the ship when pitching is upward?

    <p>Moves toward star-board</p> Signup and view all the answers

    What is the effect of the reactive gyroscopic couple in an airplane during a left-hand turn?

    <p>Raises the bow and lowers the stern</p> Signup and view all the answers

    What is the direction of the active gyroscopic couple in an airplane during a left-hand turn?

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

    When an airplane takes a left turn, what happens to the plane of active gyroscopic couple?

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

    What is the angular momentum vector direction changed to in an airplane by the active gyroscopic couple?

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

    What represents the change of angular momentum or active gyroscopic couple in an airplane during a left turn?

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

    In naval ship terminology, what are the left hand and right hand sides called when viewed from the stern?

    <p>'Port' and 'Star-board'</p> Signup and view all the answers

    What is the angular velocity of precession denoted by?

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

    Which plane is referred to as the plane of precession in the text?

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

    What represents the active gyroscopic couple in the horizontal plane?

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

    In what direction does the active gyroscopic couple act in the plane XOY?

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

    What is the axis of active gyroscopic couple perpendicular to?

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

    What is the reactive gyroscopic couple opposite in direction to?

    <p>Active gyroscopic couple</p> Signup and view all the answers

    In which devices are gyroscopes commonly used according to the text?

    <p>Ships, aero planes, monorail cars, gyrocompasses, etc.</p> Signup and view all the answers

    What is used to minimize the rolling and pitching effects of waves in ships?

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

    In which plane does the axis OX rotate when seen from the top?

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

    What is known as the axis of spin according to the text?

    <p>Axis OX'</p> Signup and view all the answers

    What condition is necessary for the effect of gyroscopic couple on a naval ship to occur?

    <p>The axis of precession should be perpendicular to the axis of spin</p> Signup and view all the answers

    Why is there no effect of gyroscopic couple acting on a naval ship during rolling?

    <p>The axis of precession is parallel to the axis of spin</p> Signup and view all the answers

    What is the formula for the velocity of precession in a vehicle taking a turn?

    <p>$P = v/R$</p> Signup and view all the answers

    In the context of a vehicle taking a turn, what does the gyroscopic couple due to 4 wheels depend on?

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

    What will happen if the sum of P/2 and Q/2 exceeds W/4 in a vehicle taking a turn?

    <p>The vehicle will overturn</p> Signup and view all the answers

    What happens if PI becomes zero or negative in a vehicle taking a turn at high speeds?

    <p>The inner wheels lose contact with the ground</p> Signup and view all the answers

    What is the effect of centrifugal force on a vehicle moving along a curved path?

    <p>It causes overturning tendency</p> Signup and view all the answers

    What balances the overturning couple in a turning vehicle?

    <p>Vertical reactions on both inner and outer wheels</p> Signup and view all the answers

    What is the angle of heel in a two-wheel vehicle when taking a turn?

    <p>Inclination of the vehicle to the vertical for equilibrium</p> Signup and view all the answers

    What is the effect of the gyroscopic couple on a two-wheel vehicle taking a turn?

    <p>Lifts the nose upwards and tail downwards</p> Signup and view all the answers

    What is the angular Momentum vector due to spin represented by in a two-wheel vehicle?

    <p>OA inclined to OX at an angle</p> Signup and view all the answers

    Which force acts horizontally through the centre of gravity in a two-wheel vehicle taking a turn?

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

    What is the Total overturning couple's role in the stability of a two-wheel vehicle?

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

    How can the value of the angle of heel be determined in a two-wheel vehicle?

    <p>$m.g.h \sin{\theta}$</p> Signup and view all the answers

    What is the mass moment of inertia of a uniform disc mounted on an arm through its center of gravity and perpendicular to its plane?

    <p>$m.r^2/2$</p> Signup and view all the answers

    How would an aeroplane be affected by the gyroscopic couple when it makes a half circle towards left?

    <p>Lifts the nose upwards and tail downwards</p> Signup and view all the answers

    What is angular velocity of precession in example 1?

    <p>16.7 rad/s</p> Signup and view all the answers

    What is the mass moment of inertia of the engine and propeller in example 2?

    <p>36 kg-m2</p> Signup and view all the answers

    What is the external force applied to a body moving along a curved path with uniform linear velocity called?

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

    What is the centrifugal force called when a body is moving with uniform linear velocity along a circular path?

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

    In precessional angular motion, what represents the change of angular velocity in time dt?

    <p>Vector xx'</p> Signup and view all the answers

    Which rule can be used to represent angular acceleration through a vector diagram?

    <p>Right hand screw rule</p> Signup and view all the answers

    What is the term for the rate of change of angular velocity with respect to time?

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

    In precessional motion, what does the vector xx' represent?

    <p>Change in angular velocity</p> Signup and view all the answers

    What is the name of the axis about which the axis of spin is going to rotate?

    <p>Axis of precession</p> Signup and view all the answers

    What is the plane called where the disc is rotating and parallel to the plane YOZ?

    <p>Plane of spinning</p> Signup and view all the answers

    What is the active gyroscopic couple needed to be applied for the disc when the axis of spin rotates with angular velocity P?

    <p>I*P</p> Signup and view all the answers

    What is the name given to the plane represented by XOY, about which the couple causing a change in angular momentum lies?

    <p>Plane of active gyroscopic couple</p> Signup and view all the answers

    What is the reactive couple that the disc experiences when the axis of spin rotates about the axis of precession called?

    <p>Reactive gyroscopic couple</p> Signup and view all the answers

    Where are gyroscopes commonly used according to the provided text?

    <p>In fighter jets</p> Signup and view all the answers

    Which vector represents an anticlockwise couple in the plane XOY as per Figure (b)?

    <p>(xx')</p> Signup and view all the answers

    What does d/dt represent in this context?

    <p>Angular velocity of precession</p> Signup and view all the answers

    What is the horizontal plane where the axis of spin rotates called?

    <p>'Plane of precession'</p> Signup and view all the answers

    'Gyroscopic Couple' refers to an applied force causing what type of motion in a spinning disc?

    <p>'Rotational motion'</p> Signup and view all the answers

    What is the angular velocity of precession in radians per second?

    <p>0.37 rad/s</p> Signup and view all the answers

    What is the gyroscopic Couple calculated to be in kilonewton-meters?

    <p>200.866 kN-m</p> Signup and view all the answers

    In which direction does the reactive gyroscopic couple effect cause the ship to move?

    <p>Raise the bow and lower the stern</p> Signup and view all the answers

    Which of the following is NOT an industrial application of gyroscopes as mentioned in the text?

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

    What does I represent in the context of the rotor's properties?

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

    What happens to the angular momentum vector when an airplane takes a left turn?

    <p>It changes direction</p> Signup and view all the answers

    In a naval ship, what is the rear end known as?

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

    What is the effect of the reactive gyroscopic couple on a naval ship when pitching is downward?

    <p>Turns the ship towards port side</p> Signup and view all the answers

    What does the active gyroscopic couple on an airplane cause during a left-hand turn?

    <p>Clockwise rotation in the OZ axis</p> Signup and view all the answers

    What is the effect of steering on a naval ship?

    <p>Left or right curve turning</p> Signup and view all the answers

    What is the role of the reactive gyroscopic couple during pitching upward of a naval ship?

    <p>Moves the ship toward star-board</p> Signup and view all the answers

    Which plane is perpendicular to vector xx' representing the active gyroscopic couple?

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

    What defines the left-hand and right-hand sides of a naval ship when viewed from the stern?

    <p>$Port$ and $Star-board$</p> Signup and view all the answers

    When an airplane makes a left turn, what is the direction of reactive gyroscopic couple?

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

    During pitching upward of a naval ship, what force does the reactive gyroscopic couple apply?

    <p>Star-board force</p> Signup and view all the answers

    What is the condition required for the effect of the gyroscopic couple on a naval ship to occur?

    <p>The axis of precession should be perpendicular to the axis of spin.</p> Signup and view all the answers

    In a vehicle moving along a curved path, what balances the overturning couple caused by the centrifugal force?

    <p>Vertical reaction on the wheels</p> Signup and view all the answers

    What happens to the vertical reactions at the wheels in a vehicle taking a turn if the sum of P/2 and Q/2 exceeds W/4?

    <p>The inner wheels leave the ground.</p> Signup and view all the answers

    What does the gyroscopic couple due to the rotating parts of the engine depend on?

    <p>Angular velocity of the engine</p> Signup and view all the answers

    What is the effect of the gyroscopic couple on the vertical reactions at the wheels in a vehicle taking a turn?

    <p>Produces reactions in opposite directions on inner and outer wheels</p> Signup and view all the answers

    What is required for a gyroscopic couple to be generated in a vehicle taking a turn?

    <p>Precession and rotating parts</p> Signup and view all the answers

    What does the magnitude of vertical reaction on each wheel depend on in a turning vehicle?

    <p>Sum of P and Q</p> Signup and view all the answers

    How does the gyroscopic couple impact the reactions on inner and outer wheels in a turning vehicle?

    <p>Outer wheels have upward reaction.</p> Signup and view all the answers

    In a two-wheel vehicle taking a turn, the angle at which the axis of spin is inclined to the horizontal is known as ____________.

    <p>Angle of heel</p> Signup and view all the answers

    What is the effect of the gyroscopic couple on a two-wheel vehicle taking a turn?

    <p>Lifts the vehicle upwards</p> Signup and view all the answers

    What is the centrifugal force that acts on a two-wheel vehicle taking a turn known as?

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

    Which term is used to describe the angular momentum vector due to spin in a two-wheel vehicle?

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

    What will happen to a ship when pitching is upward?

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

    What is the name for the force that balances the overturning couple in a turning vehicle?

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

    What is the angle used to determine the vehicle's stability in relation to the balancing and overturning couple?

    <p>Angle of heel</p> Signup and view all the answers

    What is used to minimize rolling and pitching effects of waves in ships?

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

    What is the term used to describe the force applied externally over a body moving along a curved path with uniform linear velocity?

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

    When a body itself is moving with uniform linear velocity along a circular path, what is the force that acts radially outward?

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

    In precessional angular motion, what is the vector quantity that represents the rate of change of angular velocity with respect to time?

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

    When a disc is spinning about an axis in anticlockwise direction, what rule can be used to represent the change in angular velocity after a short interval of time?

    <p>Right hand rule</p> Signup and view all the answers

    In the context of a spinning disc, what does the vector xx' represent?

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

    What is the term used to describe the force required to make a body move along a required curved path with uniform linear velocity?

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

    What is the direction of the reactive gyroscopic couple effect when the ship steers to the left with the rotor rotating clockwise when viewed from the stern?

    <p>Raise the bow and lower the stern</p> Signup and view all the answers

    Which unit is used to express the gyroscopic couple calculated in the given scenario?

    <p>kN-m</p> Signup and view all the answers

    What does the application of gyroscopes in inertial navigation systems and submarines emphasize?

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

    In what type of motion does the reactive gyroscopic couple result when an airplane makes a left turn?

    <p>Raises the nose and lowers the tail</p> Signup and view all the answers

    What role do gyroscopes play in maintaining direction in tunnel mining according to the text?

    <p>Navigate through tunnels accurately</p> Signup and view all the answers

    What is the effect of the reactive gyroscopic couple on a naval ship during pitching upward?

    <p>Move the ship toward starboard</p> Signup and view all the answers

    What does the active gyroscopic couple on a naval ship cause during steering?

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

    When an airplane takes a left turn, what is the direction of the active gyroscopic couple?

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

    What does the vector xx' represent in the context of an airplane taking a left turn?

    <p>Change of angular momentum</p> Signup and view all the answers

    In a naval ship, what is the right-hand side called when viewed from the stern?

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

    What is the effect of reactive gyroscopic couple in an airplane during pitching downward?

    <p>Turn the aircraft towards port side</p> Signup and view all the answers

    What happens if a ship pitches downward due to reactive gyroscopic couple?

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

    What is the effect of an active gyroscopic couple on an airplane during pitching upward?

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

    What does the plane of active gyroscopic couple XOY represent when it is vertical as shown in Fig (b)?

    <p>Perpendicular to xx'</p> Signup and view all the answers

    What is the effect of reactive gyroscopic couple during pitching upward on a naval ship?

    <p>Turns towards port side</p> Signup and view all the answers

    What is the net gyroscopic couple acting on a vehicle with 4 wheels when the rotating parts of the engine and wheels rotate in the same direction?

    <p>$W.P(4IW + G.IE)$</p> Signup and view all the answers

    In a vehicle moving along a curved path, what is the magnitude of the vertical reaction at each outer or inner wheel due to the gyroscopic couple?

    <p>$C/2x$</p> Signup and view all the answers

    What is the role of the vertical reactions at the outer and inner wheels in a vehicle moving at high speeds and PI becoming zero or negative?

    <p>Causing the outer wheels to leave the ground</p> Signup and view all the answers

    What happens if the sum of P/2 and Q/2 exceeds W/4 in a vehicle taking a turn?

    <p>Overturning of the vehicle</p> Signup and view all the answers

    Which statement accurately describes the vertical reactions at the outer and inner wheels due to centrifugal force acting on a vehicle along a curved path?

    <p>$Q = W/2$</p> Signup and view all the answers

    What is required for a gyroscopic couple to be generated in a vehicle taking a turn?

    <p>Perpendicularity between axis of precession and spin axis</p> Signup and view all the answers

    What is the primary purpose of the gyroscopic couple acting on a vehicle moving along a curved path?

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

    How does the centrifugal force affect the stability of a vehicle taking a turn?

    <p>Increases overturning tendency</p> Signup and view all the answers

    Which factor determines whether an automobile's inner wheels will leave the ground during high-speed turns?

    <p>$P/2$ exceeding $W/4$</p> Signup and view all the answers

    What is the magnitude of Total overturning couple in a vehicle moving along a curved path?

    <p>Balanced by vertical reactions on wheels</p> Signup and view all the answers

    What is the angular velocity of the axis of spin about the axis of precession known as?

    <p>Angular velocity of precession</p> Signup and view all the answers

    Which vector represents the active gyroscopic couple causing a change in angular momentum?

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

    What is the plane called where the active gyroscopic couple lies?

    <p>Plane of procession</p> Signup and view all the answers

    What is the axis about which the active gyroscopic couple acts called?

    <p>Axis of active gyroscopic couple</p> Signup and view all the answers

    In which direction does the vector xx' representing the active gyroscopic couple act?

    <p>Perpendicular to OY</p> Signup and view all the answers

    Which plane is known as the plane of precession?

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

    What is the reactive couple experienced by the disc when the axis of spin rotates about the axis of precession known as?

    <p>Reactive gyroscopic couple</p> Signup and view all the answers

    What is used in ships to minimize rolling and pitching effects caused by waves?

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

    What is the effect of the gyroscopic couple on a vehicle taking a turn?

    <p>Causes the vehicle to lean inwards towards the turn</p> Signup and view all the answers

    In a two-wheel vehicle, what determines the stability in relation to balancing and overturning couples?

    <p>Height of the centre of gravity</p> Signup and view all the answers

    What is the role of the centrifugal force in a two-wheel vehicle taking a turn?

    <p>Acts vertically through the center of gravity</p> Signup and view all the answers

    What is the effect of the reactive gyroscopic couple in an airplane making a left turn?

    <p>Lifts the tail upwards</p> Signup and view all the answers

    What represents the gyroscopic couple on an aircraft during a left-hand turn?

    <p>Total overturning couple</p> Signup and view all the answers

    How does the angle of heel impact the stability of a two-wheel vehicle?

    <p>Enhances stability during sharp turns</p> Signup and view all the answers

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