Centripetal and Centrifugal Forces in Circular Motion
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Questions and Answers

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

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

    • What is the force that acts radially outwards on a body moving with uniform linear velocity along a circular path?

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

    • Which type of motion involves the action of reactive or centrifugal force to tilt or move the body in a radially outward direction?

  • Circular motion
  • Linear motion
  • Angular motion (correct)
  • Rectilinear motion

    • How can angular acceleration be represented visually?

    <p>By drawing a vector diagram with the right hand screw rule</p> Signup and view all the answers

    What does the vector xx' represent in the context of angular motion?

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

    In which direction does the centrifugal force act on a body moving with uniform linear velocity along a circular path?

    <p>Radially outwards</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 when the rotor rotates in a clockwise direction and the ship steers to the left?

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

    How are the bow and stern affected by the reactive gyroscopic couple when the rotor rotates clockwise and the ship steers to the left?

    <p>Bow raises and stern lowers</p> Signup and view all the answers

    In which application are gyroscopes used to maintain direction in tunnel mining?

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

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

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

    In which direction does the active gyroscopic couple act?

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

    What is the name of the axis about which the axis of spin rotates?

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

    What is the effect of the reactive gyroscopic couple on a disc when the axis of spin rotates about the axis of precession?

    <p>It opposes the active gyroscopic couple</p> Signup and view all the answers

    What is the plane XOY referred to as?

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

    What is the vector xx' in relation to the gyroscopic principle?

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

    Which plane is called the plane of spinning in gyroscopic systems?

    <p>'Horizontal plane XOZ'</p> Signup and view all the answers

    'Angular momentum' is represented by which vector on the disc?

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

    In the context of a two-wheel vehicle taking a turn, what is the angle known as when the vehicle is inclined at an angle with the vertical plane?

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

    What is the formula for calculating the velocity of precession when a two-wheel vehicle moves over a curved path?

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

    When a two-wheel vehicle is turning, what is the effect of the centrifugal couple?

    <p>It tends to overturn the vehicle.</p> Signup and view all the answers

    What is the formula for calculating the balancing couple required for stability in a turning two-wheel vehicle?

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

    In Example 1, what is the mass moment of inertia (I) of the uniform disc mounted on an arm?

    <p>$0.056$ kg-m²</p> Signup and view all the answers

    In Example 2, what is the effect of the gyroscopic couple on the aircraft when it makes a half circle?

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

    What is the angular velocity of precession in Example 3 of the ship turbine rotor?

    <p>$1.11$ rad/s</p> Signup and view all the answers

    How does the gyroscopic couple affect the ship's turbine rotor in Example 3 when it steers to the left?

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

    What is the gyroscopic couple acting on an aeroplane in Example 2 when it rotates at 2400 rpm?

    <p>$10.046$ kN-m</p> Signup and view all the answers

    If a two-wheel vehicle is inclined with an angle of heel of $45^{ ext{o}}$, what value does this angle represent according to the text?

    <p>$45^{ ext{o}}$ inclination from horizontal axis</p> Signup and view all the answers

    What effect does the active gyroscopic couple have on an airplane during a left turn?

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

    What is the effect of the reactive gyroscopic couple on a naval ship during a left turn?

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

    Which direction is the active gyroscopic couple on an airplane during a left turn according to the text?

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

    In which direction will the reactive gyroscopic couple act on an airplane during a left turn?

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

    What is the effect of the active gyroscopic couple on a naval ship during steering?

    <p>Changes angular momentum vector from ox to ox'</p> Signup and view all the answers

    During pitching of a naval ship, what effect does the reactive gyroscopic couple have when the pitching is upward?

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

    What happens to the ship's movement when pitching downward with respect to the reactive gyroscopic couple?

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

    How does the rotor's rotation direction affect a ship's angular momentum vector in steering?

    <p>Determines its initial direction (ox)</p> Signup and view all the answers

    'The plane of active gyroscopic couple XOY will be perpendicular to xx', i.e. vertical in this case.' - Which figure shows this relationship?

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

    What is meant by 'pitching' in naval terms?

    <p>Vertical movement up and down</p> Signup and view all the answers

    In the context of a naval ship rolling, when will there be no effect of the gyroscopic couple?

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

    What is the formula for the net gyroscopic couple (C) acting on a vehicle moving along a curved path?

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

    What reaction will be produced on the road surface due to the gyroscopic couple in a vehicle taking a turn?

    <p>Vertically upwards on outer wheels and downwards on inner wheels</p> Signup and view all the answers

    Which situation would tend to overturn an automobile while in motion?

    <p>Sum of vertical reactions at inner wheels greater than total weight</p> Signup and view all the answers

    What is the condition for the contact between inner wheels and the ground to be maintained during high-speed motion?

    <p>$P/2 + Q/2 &gt; W/4$</p> Signup and view all the answers

    What is the formula for the vertical reaction at each outer or inner wheel due to the gyroscopic couple?

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

    What happens when PI may be zero or negative in a vehicle moving at high speeds?

    <p>$P/2 &lt; 0$, inner wheels leave the ground</p> Signup and view all the answers

    What causes vertical reactions that are vertically upwards on outer wheels and downwards on inner wheels in a vehicle taking a turn?

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

    Which component balances the overturning couple in a vehicle moving along a curved path?

    <p>$Q/2$ at outer wheels</p> Signup and view all the answers

    What determines whether a positive or negative sign is used in the formula for net gyroscopic couple acting on a vehicle?

    <p>Direction of rotation between wheels and engine</p> Signup and view all the answers

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