Angular and Linear Acceleration in Rigid Bodies
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Questions and Answers

What type of analysis involves the evaluation of input forces, joint forces, and motion of members?

  • Kinetic force analysis
  • Static force analysis
  • Inertial force analysis
  • Dynamic force analysis (correct)

What is the relationship between inertia force and accelerating force?

  • Inertia force is opposite in direction to the accelerating force
  • Inertia force is less than the accelerating force
  • Inertia force is equal in magnitude to the accelerating force (correct)
  • Inertia force is greater than the accelerating force

What is the formula for inertia force where 'm' is the mass of the body and 'a' is the linear acceleration?

  • $Inertia force = m \times a$
  • $Inertia force = -m \times a$
  • $Inertia force = -m/a$ (correct)
  • $Inertia force = m/a$

What does the inertia torque do when applied to a rigid body?

<p>Brings the body in an equilibrium position (D)</p> Signup and view all the answers

How can a system of forces acting on a rigid body be reduced for analysis?

<p>To a single resultant force (B)</p> Signup and view all the answers

What do two equal and opposite forces acting through the center of gravity of a body create?

<p>A couple and a parallel force (C)</p> Signup and view all the answers

What is the formula for moment of inertia of a body about an axis passing through its centre of gravity and perpendicular to the point in which a couple acts?

<p>I = m * k^2 (D)</p> Signup and view all the answers

In a rigid body, what does the equal and opposite force -m.a represent according to D-Alembert's Principle?

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

What are V-threads mainly used for?

<p>Preventing the nut from slackening (C)</p> Signup and view all the answers

What is the distance between the top and bottom surfaces of a screw thread known as?

<p>Depth of thread (C)</p> Signup and view all the answers

What is the main advantage of V-threads over square threads?

<p>Increased frictional resistance (A)</p> Signup and view all the answers

What is the curve traced by a particle while moving along a screw thread called?

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

If the lead of a screw is equal to its pitch, what type of screw is it?

<p>Single-threaded screw (A)</p> Signup and view all the answers

'FI' in D-Alembert's Principle stands for:

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

'H' in the formula 'F × h' represents:

<p>'H' as perpendicular distance between force and center of gravity (C)</p> Signup and view all the answers

What type of force acts at the circumference of the rotating shaft?

<p>Frictional force (C)</p> Signup and view all the answers

In order for rotation to be maintained, what must be present?

<p>A couple rotating the shaft (A)</p> Signup and view all the answers

What is the relationship between the resultant force and weight (W) for uniform motion?

<p>R = W (B)</p> Signup and view all the answers

What is the formula for the frictional torque (T) when the shaft rotates with angular velocity rad/s?

<p>$T = µ.W.r$ (C)</p> Signup and view all the answers

What is used to take the axial thrust of rotating shafts?

<p>Pivots and collar bearings (A)</p> Signup and view all the answers

What type of bearing surface is most commonly used for collars in modern practice?

<p>Flat bearing surface (C)</p> Signup and view all the answers

What is assumed in the study of friction of bearings regarding pressure distribution?

<p>Pressure is uniformly distributed (C)</p> Signup and view all the answers

What does a flat pivot bearing (foot step bearing) support?

<p>$W = \text{Load transmitted over the bearing surface}$ (C)</p> Signup and view all the answers

What does the intensity of wear depend on in a bearing?

<p>$v = \text{Velocity of rubbing surfaces}$ (D)</p> Signup and view all the answers

What is responsible for reducing pressure intensity along rubbing surfaces in bearings?

<p>Multiple pivots at different radii (B)</p> Signup and view all the answers

In collar bearings, what is another common term used to refer to them?

<p>Thrust bearings (B)</p> Signup and view all the answers

What is the formula to calculate the total frictional torque on a collar bearing?

<p>$\int_{r2}^{r1} \left(\dfrac{CdA}{r}\right)$ (B)</p> Signup and view all the answers

What is the power absorbed in friction at the thrust block for uniform pressure in Example 1?

<p>26.4 kW (A)</p> Signup and view all the answers

If a shaft has an external collar diameter of 400 mm and shaft diameter of 250 mm, what is the internal collar diameter (r2) in mm?

<p>125 (C)</p> Signup and view all the answers

What is the coefficient of friction used in Example 2 for estimating the power absorbed?

<p>0.35 (B)</p> Signup and view all the answers

In Example 2, what is the calculated number of collars required for the given scenario?

<p>6 (C)</p> Signup and view all the answers

What is the relationship between the rate of wear and the intensity of pressure and velocity of rubbing surfaces?

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

What does the intensity of normal pressure vary inversely with in the case of uniform wear?

<p>Distance from the central axis (A)</p> Signup and view all the answers

What is the power lost in friction estimated based on in the given example?

<p>Uniform pressure distribution and coefficient of friction (A)</p> Signup and view all the answers

What does a conical pivot bearing support according to the provided text?

<p>A shaft carrying a load (B)</p> Signup and view all the answers

What is the semi angle of the cone in a conical pivot bearing supporting a load?

<p>60 degrees (A)</p> Signup and view all the answers

In a trapezoidal or truncated conical pivot bearing, what is considered when calculating total torque on the bearing?

<p>External and internal radius (A)</p> Signup and view all the answers

What is the total load transmitted to the ring in case of uniform wear with an external and internal radius in a frustum of a cone?

<p>$2ig(rac{C}{r}ig)dr$ (C)</p> Signup and view all the answers

What does the power absorbed in friction depend on in collar bearings?

<p>Axial thrust of rotating shafts (A)</p> Signup and view all the answers

What is used to take the axial thrust of rotating shafts according to the text?

<p>Flat Collar Bearing (A)</p> Signup and view all the answers

In uniform wear problems, what is assumed to be uniform?

<p>Pressure distribution (B)</p> Signup and view all the answers

What is placed on the head of the square threaded rod in a screw jack?

<p>Load to be raised or lowered (D)</p> Signup and view all the answers

What is the coefficient of friction, denoted by µ, between the screw and nut?

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

In a V-thread (acme or trapezoidal threads), why is the normal reaction between the screw and nut increased?

<p>Axial load W is increased (D)</p> Signup and view all the answers

What does the coefficient of friction µ1 represent in a journal bearing?

<p>Coefficient of friction for the collar (C)</p> Signup and view all the answers

What is the total torque required to overcome friction when an effort P1 is applied at the end of a lever?

<p>$W tan(a + f)$ (B)</p> Signup and view all the answers

Which force acts downwards in a screw jack when lifting a load?

<p>$µ.RN$ (C)</p> Signup and view all the answers

What represents the reaction RN in an inclined plane similar to that of a screw jack?

<p>$W cosa$ (D)</p> Signup and view all the answers

What is meant by point A in relation to a journal bearing?

<p>[point A] is known as seat or point of pressure (B)</p> Signup and view all the answers

What kind of pair does a journal bearing form with its fixed outer element?

<p>[Journal bearing forms] a turning pair (C)</p> Signup and view all the answers

What is required to overcome the friction at the collar in a screw jack?

<p>Coefficient of friction µ1 for the collar (C)</p> Signup and view all the answers

Flashcards

Dynamic Force Analysis

Dynamic force analysis evaluates forces acting on a body in motion, considering input forces, joint forces, and member motion.

Inertia Force

The inertia force is equal in magnitude but opposite in direction to the accelerating force acting on a body.

Inertia Force Formula

Inertia force is calculated as the negative product of mass (m) and linear acceleration (a).

Inertia Torque

Inertia torque brings a rigid body to an equilibrium position by counteracting any unbalanced forces causing rotation.

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Resultant Force

A system of forces acting on a rigid body can be simplified into a single resultant force that represents the combined effect of all the forces.

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Couple and Parallel Force

Two equal and opposite forces acting through the center of gravity of a body create a couple, which causes rotation, and a parallel force which causes translation.

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Moment of Inertia Formula

The moment of inertia of a body about an axis passing through its center of gravity is given by I = m * k^2, where 'm' is mass and 'k' is the radius of gyration.

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D'Alembert's Principle

According to D'Alembert's Principle, the fictitious inertia force (-m.a) represents the equal and opposite force to the actual force acting on a rigid body.

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V-threads (Acme Threads)

V-threads are primarily used to prevent the nut from loosening due to vibration or load changes.

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Depth of Thread

The depth of thread is the vertical distance between the top and bottom surfaces of a screw thread.

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V-thread Advantage

V-threads offer greater frictional resistance compared to square threads, making them more secure against loosening.

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Helix

The curve traced by a particle moving along a screw thread is called a helix.

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Single-threaded Screw

A single-threaded screw has a lead equal to its pitch, meaning it advances one pitch per revolution.

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FI in D'Alembert's Principle

In D'Alembert's Principle, 'FI' stands for 'Fictitious Inertia', representing the inertia force.

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H in Force x Distance Formula

In the formula 'F × h', 'H' represents the perpendicular distance between the force (F) and the center of gravity (G).

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Frictional Force on Shaft

Frictional force acts at the circumference of a rotating shaft, resisting its motion.

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Couple for Rotation

For rotation to be maintained, a couple must be present to overcome the frictional torque and keep the shaft rotating.

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Resultant Force and Weight

In uniform motion, the resultant force (R) acting on a body is equal to its weight (W).

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Frictional Torque Formula

Frictional torque (T) on a rotating shaft is calculated as T = µ.W.r, where µ is the coefficient of friction, W is the weight, and r is the radius.

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Pivots and Collar Bearings

Pivots and collar bearings are used to support the axial thrust of rotating shafts.

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Flat Collar Bearing Surface

Modern practice often utilizes a flat bearing surface for collars, providing simpler design and manufacturing.

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Uniform Pressure Distribution

In studying bearing friction, pressure distribution is usually assumed uniform for simpler analysis.

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Flat Pivot Bearing

A flat pivot bearing, also known as a foot step bearing, supports a load (W) transmitted through the bearing surface.

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Wear Intensity

The intensity of wear in a bearing depends on the velocity of rubbing surfaces (v).

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Multiple Pivots for Reduced Wear

Multiple pivots at different radii reduce pressure intensity along rubbing surfaces, resulting in less wear.

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Collar Bearing and Thrust Bearing

Collar bearings are also known as thrust bearings, as they are designed to support axial loads.

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Total Frictional Torque

The total frictional torque on a collar bearing is calculated by integrating the frictional torque over the bearing surface.

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Power Absorbed in Friction (Example 1)

Power absorbed in friction at the thrust block for uniform pressure can be calculated using specific formulas involving thrust, friction, and speed.

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Internal Collar Diameter

The internal collar diameter (r2) is calculated by subtracting the shaft diameter from the external collar diameter.

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Coefficient of Friction

The coefficient of friction (µ) used in calculations is a property of the materials in contact and determines the amount of friction.

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Number of Collars (Example 2)

The number of collars required is determined by the load and the bearing design, ensuring sufficient load distribution.

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Rate of Wear

Rate of wear is directly proportional to both the intensity of pressure and the velocity of rubbing surfaces in bearing.

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Pressure Distribution in Uniform Wear

In uniform wear, the intensity of normal pressure varies inversely with the distance from the central axis.

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Power Loss in Friction

Power lost in friction is estimated based on the assumed uniform pressure distribution and the coefficient of friction.

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Conical Pivot Bearing

A conical pivot bearing supports a shaft carrying a load, using a conical shape for load distribution.

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Conical Pivot Bearing Angle

The semi-angle of the cone in a conical pivot bearing supporting a load is typically 60 degrees.

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Total Torque in Trapezoidal Bearing

In a trapezoidal or truncated conical pivot bearing, the total torque is calculated by considering both the external and internal radius of the bearing surface.

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Total Load in Frustum of Cone

The total load transmitted to the ring in case of uniform wear with an external and internal radius in a frustum of a cone is calculated using a specific formula involving radius.

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Power Absorbed in Friction (Collar Bearings)

Power absorbed in friction in collar bearings depends on the axial thrust of rotating shafts, friction coefficient, and speed.

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Axial Thrust Support

Flat collar bearings are used to take the axial thrust of rotating shafts, supporting the shaft from moving sideways.

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Uniform Wear Assumption

In uniform wear problems, the pressure distribution is assumed to be uniform, meaning the load is spread evenly over the bearing surface.

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Load in Screw Jack

The load to be raised or lowered is placed on the head of the square threaded rod in a screw jack.

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Coefficient of Friction in Screw Jack

The coefficient of friction (µ) between the screw and nut is represented by tan ø, where ø is the friction angle.

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Normal Reaction in V-threads

In V-threads, the normal reaction (RN) between the screw and nut is increased due to the increased axial load (W).

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Coefficient of Friction (µ1)

The coefficient of friction µ1 represents the coefficient of friction for the collar in a journal bearing, affecting the frictional torque.

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Total Torque in Screw Jack

The total torque required to overcome friction, when an effort P1 is applied at the end of a lever, is calculated by accounting for the load, angle, and friction

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Downward Force in Screw Jack

The downward force in a screw jack, when lifting a load, is represented by µ.RN, where µ is the coefficient of friction and RN is the normal reaction.

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Reaction in Inclined Plane

In an inclined plane similar to that of a screw jack, the reaction RN is represented by W cosa, where W is the load and a is the angle of inclination.

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Point A in Journal Bearing

Point A, also known as the seat or point of pressure, is the contact point between the journal and the bearing surface in a journal bearing.

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Journal Bearing as a Pair

A journal bearing forms a turning pair with its fixed outer element, allowing the inner element (journal) to rotate freely.

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