Centripetal and Centrifugal Forces in Circular Motion

Play an AI-generated podcast conversation about this lesson

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?

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

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

Change in angular velocity in time dt 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?

Radially outwards Signup and view all the answers

What is the mass moment of inertia of the rotor?

2880 kg-m^2 Signup and view all the answers

What is the angular velocity of precession?

0.37 rad/s 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?

200.866 kN-m 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?

Bow raises and stern lowers Signup and view all the answers

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

Submerged submarine Signup and view all the answers

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

Angular precession Signup and view all the answers

In which direction does the active gyroscopic couple act?

Plane XOY Signup and view all the answers

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

Axis OY 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?

It opposes the active gyroscopic couple Signup and view all the answers

What is the plane XOY referred to as?

Plane of active gyroscopic couple Signup and view all the answers

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

Change in angular momentum Signup and view all the answers

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

'Horizontal plane XOZ' Signup and view all the answers

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

'ox'' 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?

Angle of heel 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 = v / R Signup and view all the answers

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

It tends to overturn the vehicle. Signup and view all the answers

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

$m.g.h \sin(\theta)$ 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?

$0.056$ kg-m² 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?

Lifts the nose upwards and tail downwards Signup and view all the answers

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

$1.11$ rad/s 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?

Raises the bow and lowers the stern Signup and view all the answers

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

$10.046$ kN-m 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?

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

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

Raises the nose and dips the tail Signup and view all the answers

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

Raises the bow and lowers the stern Signup and view all the answers

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

Clockwise Signup and view all the answers

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

Counterclockwise Signup and view all the answers

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

Changes angular momentum vector from ox to ox' 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?

Moves the ship toward star-board side Signup and view all the answers

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

Turns towards port side Signup and view all the answers

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

Determines its initial direction (ox) 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?

(a) Signup and view all the answers

What is meant by 'pitching' in naval terms?

Vertical movement up and down Signup and view all the answers

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

When the axis of precession is parallel to the axis of spin 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?

$W.P(4 IW + G.IE)$ 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?

Vertically upwards on outer wheels and downwards on inner wheels Signup and view all the answers

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

Sum of vertical reactions at inner wheels greater than total weight 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?

$P/2 + Q/2 > W/4$ 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?

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

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

$P/2 < 0$, inner wheels leave the ground 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?

Centrifugal force Signup and view all the answers

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

$Q/2$ at outer wheels 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?

Direction of rotation between wheels and engine Signup and view all the answers