Centripetal and Centrifugal Forces in Circular Motion

49 Questions

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

Centripetal force

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

Centrifugal force

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

Angular motion

How can angular acceleration be represented visually?

By drawing a vector diagram with the right hand screw rule

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

Change in angular velocity in time dt

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

Radially outwards

What is the mass moment of inertia of the rotor?

2880 kg-m^2

What is the angular velocity of precession?

0.37 rad/s

What is the gyroscopic couple when the rotor rotates in a clockwise direction and the ship steers to the left?

200.866 kN-m

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

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

Submerged submarine

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

Angular precession

In which direction does the active gyroscopic couple act?

Plane XOY

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

Axis OY

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

What is the plane XOY referred to as?

Plane of active gyroscopic couple

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

Change in angular momentum

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

'Horizontal plane XOZ'

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

'ox''

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

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

P = v / R

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

It tends to overturn the vehicle.

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

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

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

$0.056$ kg-m²

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

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

$1.11$ rad/s

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

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

$10.046$ kN-m

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

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

Raises the nose and dips the tail

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

Raises the bow and lowers the stern

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

Clockwise

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

Counterclockwise

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

Changes angular momentum vector from ox to ox'

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

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

Turns towards port side

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

Determines its initial direction (ox)

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

(a)

What is meant by 'pitching' in naval terms?

Vertical movement up and down

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

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

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

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

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

Sum of vertical reactions at inner wheels greater than total weight

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

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

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

$P = C/2x$

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

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

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