2A1 Chapter 9 Angular Motion

2nd Class Power Engineering

What is angular displacement?

The angle through which a rotating body moves, measured in radians.

What is the unit of angular velocity?

Radians per second (rad/s).

What is a scalar quantity that describes the angular distance moved in a given time interval?

Angular velocity

What is a scalar quantity that describes the change in angular velocity in a given time interval?

Angular acceleration

What is the conventional symbol for angular acceleration?

α (alpha).

What is the formula for calculating the moment of inertia for a rotating disk?

I = mr², where m is mass and r is radius.

What is an equivalent radius at which the mass of an object can be assumed to be concentrated?

Radius of gyration

What is a measure of the force that can cause an object to rotate about an axis?

Torque

What is the relationship between torque and moment of inertia?

Torque = Moment of inertia × Angular acceleration.

Define brake power.

The power of an engine measured at the output shaft. It is normally referred to as “brake power” because a device called a rope brake is often used to measure the power.

What is mechanical efficiency?

The ratio of useful work output to total work input, expressed as a percentage.

How is power transmitted by a belt drive calculated?

Power = Torque × Angular velocity.

What is the apparent force that draws a rotating body away from the center of rotation?

Centrifugal force

What is the force that acts on a body moving in a circular path, directed towards the center of rotation?

Centripetal force

What is centripetal acceleration?

The acceleration directed towards the center of a circular path, calculated as v²/r, where v is linear velocity and r is radius.

How do you convert angular displacement from radians to revolutions?

Revolutions = Angular displacement (rad) / (2π rad/rev).

What is the significance of the diameter of a pulley in angular motion calculations?

It does not affect the answers for angular displacement, velocity, or acceleration, as these depend on angular measures.

What is the formula for calculating the average angular velocity during a run down?

Average angular velocity = (Initial angular velocity + Final angular velocity) / 2.

What is the formula for the moment of inertia (I) of a flywheel?

I = mr², where m is mass and r is the radius of the flywheel.

How is the radius of gyration (k) related to the moment of inertia?

k = √(I/m), where I is the moment of inertia and m is mass.

What are the units of torque?

Newton meters (Nm).

What happens to torque if the force acts through the center of rotation?

The torque will be zero.

What is the formula for torque when mass is concentrated at the radius of gyration?

T = m × k × α, where k is the radius of gyration.

What is the kinetic energy (K) formula for rotating masses?

K = 1/2 × I × ω², where I is the moment of inertia and ω is angular velocity.

What is the formula for work (W) done by a rotating body for one revolution?

W = F × r × 2π.

What is the formula for power (P) related to torque (T) and angular velocity (ω)?

P = T × ω.

What is brake power (P) in terms of mass (m), gravity (g), and spring balance force (S)?

P_brake = (mg - S) × r × (2π/60).

What is the relationship between torque and angular acceleration?

Torque is analogous to force, and angular acceleration is analogous to linear acceleration.

What is the formula for calculating torque when a force is applied at radius L?

T = F × L.

What is the significance of the radius of gyration in angular motion?

It helps in calculating the moment of inertia for bodies that are not concentrated at the rim.

How is the work done by a rotating body calculated for multiple revolutions?

W = T × θ, where θ is the angle in radians.

What is the relationship between linear and angular versions of Newton's Second Law?

Torque is analogous to force, moment of inertia is analogous to mass.

What is the effect of applying a force in a direction other than tangential to the radius?

The tangential component must be determined to calculate torque.

What is the formula for brake power measured by the rope brake?

P_brake = (π n (mg * S - F)) / 60

How is mechanical efficiency calculated?

η = (P_brake / P_indicated) * 100

What is the formula for power transmitted by a belt drive?

P = (F₁ - F₂) x 2π r n / 60

What factors affect power transmission in a belt drive?

Belt tension, surface area of contact, and pulley speed.

How does belt thickness affect power transmission?

Increased belt thickness raises the effective radius, increasing power transmitted.

How can centripetal and centrifugal forces be calculated?

Using Newton's Second Law: F = m a, where a can be expressed as v²/r or ω² r.

What is the formula for centripetal acceleration?

a_c = v² / r or a_c = ω² * r

What units are used for centripetal acceleration?

m/s²

What is the relationship between linear velocity and angular velocity?

v = r * ω

What happens to velocity in circular motion?

Velocity changes direction even if speed remains constant.

What is the effect of unbalanced forces on an object in motion?

It causes the object to change its state of motion.

What is the role of friction in power transmission by belt drives?

Friction prevents slipping and ensures the belt transmits power effectively.

What is the significance of the radius in power calculations for pulleys?

It affects the torque and power transmitted by the pulley.

What is the relationship between tension on the tight and slack sides of a belt?

The effective driving force is the difference between the two tensions.

What happens to the power transmitted if the radius of the pulley increases?

It increases due to a larger effective radius.

What is the formula for calculating the change in velocity in circular motion?

Δv = r * θ

What is the relationship between angular acceleration and linear acceleration?

Angular acceleration is related to linear acceleration by the radius of the circular path.

What does Newton's first law of motion state?

An object in motion stays in motion unless acted upon by an unbalanced force.

How does the tension in a belt affect the power transmitted?

Higher tension on the tight side increases the power transmitted.

What is the centripetal force formula?

F_c = m a_c = m (ω²r), where m is mass.

What is the centrifugal force on a rotating mass?

F_c = m * ω²r, where m is mass, ω is angular velocity, and r is radius.

What is a governor in mechanical engineering?

A governor is a device used to control the speed of an engine, originally introduced by Isaac Watt.

How does a mechanical governor operate?

As speed increases, the governor's bobs move outward due to centrifugal force, adjusting the throttle valve.

What is the relationship between the height of a governor and speed?

The height of the governor is determined by the speed and is independent of the mass of the bob.

What is the formula for calculating the height of a governor?

Height (h) = (ω² * r) / g, where ω is angular velocity, r is radius, and g is acceleration due to gravity.

What happens if rotating masses are not balanced?

Unbalanced rotating masses create excessive vibration and can cause major damage.

How can you balance a single rotating mass?

By placing an equal mass at the opposite location and the same distance from the center of rotation.

What is the moment of force for a rotating mass?

The moment of force is calculated as m * r, where m is mass and r is the radius.

What is the kinetic energy formula for a rotating mass?

Kinetic energy (KE) = 0.5 I ω², where I is the moment of inertia.

What is the mechanical efficiency of an engine lifting a mass?

Mechanical efficiency = (Output power / Input power) × 100%.

What is the difference between centripetal and centrifugal force?

Centripetal force acts towards the center of rotation, while centrifugal force appears to act outward on a mass in a rotating system.

What is the compensating mass required for balance?

The compensating mass is calculated based on the moments of the unbalanced masses.

What is the formula for calculating centrifugal force on a blade?

F_c = m ω² r, where m is the mass of the blade, ω is angular velocity, and r is the distance from the center.

What is the importance of overspeed protection in rotating machinery?

Overspeed protection prevents mechanical failure by limiting the speed of rotating components.

How do you calculate the power transmitted by a pulley?

Power transmitted = (Tight side tension - Slack side tension) × Velocity of the belt.

What is the significance of the radius in balancing multiple rotating masses?

It affects the moment of force, which is crucial for achieving balance in multiple rotating masses.