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

What is the mass moment of inertia of the rotor?

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

What is the angular velocity of precession?

<p>0.37 rad/s (B)</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 (A)</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 (D)</p> Signup and view all the answers

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

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

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

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

In which direction does the active gyroscopic couple act?

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

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

<p>Axis OY (D)</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 (A)</p> Signup and view all the answers

What is the plane XOY referred to as?

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

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

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

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

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

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

<p>'ox'' (B)</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 (B)</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 (A)</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. (D)</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>$m.g.h \sin(\theta)$ (D)</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 (A)</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 (D)</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 (A)</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 (A)</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 (B)</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 (D)</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 (D)</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 (C)</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 (D)</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 (D)</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' (C)</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 (A)</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 (C)</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) (A)</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) (B)</p> Signup and view all the answers

What is meant by 'pitching' in naval terms?

<p>Vertical movement up and down (B)</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 (D)</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>$W.P(4 IW + G.IE)$ (A)</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 (A)</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 (A)</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>$P/2 + Q/2 &gt; W/4$ (A)</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>$P = C/2x$ (D)</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 (C)</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 (D)</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 (C)</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 (B)</p> Signup and view all the answers

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