p6 A

ROTATIONAL EQUILIBRIUM

When the sum of all moments (net moment) acting on the object is zero.

MOMENT (M)

A vector quantity that describes how much a force acting on an object tends to make that object rotate

about an axis (or pivot)

LEVER ARM (L)

LEVER ARM (L)

The perpendicular distance between the pivot and the force

non-concurrent forces are applied

The conditions of translational and rotational equilibrium are both

considered when

Roller, pin, fixed support

Types of support and their corresponding reaction forces:

System

is a small portion of the universe, it may be:

• a single object/particle

• a collection of objects/particles

• a region of space (eg interior of an engine)

• varying in size and shape with time

(eg rubber ball deforming when bounced)

environment

A system can be analyzed by setting a boundary to separate it from its

Work (W)

is a function of the force parallel to the direction of displacement

force of friction

is the resistance of an object either on the surface or in a viscous medium such as air or water.

force of static friction

keeps an object, which is acted upon by a force, from moving.

The force of kinetic friction is the friction force for an object in motion.

friction force of an object

is opposite to its motion or impending motion relative to the surface.

point of application of the force

For rigid bodies, displacement is measured from the

ON THE SAME DIRECTION

Work is Positive if both vectors are

On ooposite direction

Work is negative if both vectors are

ON THE SYSTEM (BY THE ENVIRONMENT)

Work is positive if done

THE SYSTEM (ON THE ENVIRONMENT)

Work is Negative if done BY

Zero

The gravitational force exerted by the sun on the earth holds the latter in an orbit around the former. Assuming the orbit is perfectly circular, the work done by this gravitational force in which the earth achieves displacement in its orbital path is:

constant

𝑊 = 𝐹⃑ % ∆ 𝑟⃑

This is only applicable if the force applied is .

Four times as much

A dart is inserted into a spring-loaded dart gun by pushing the

spring in by a distance x. For the next loading, the spring is

compressed a distance 2x. How much work is required to load

the second dart compared with that required to load the first?

kinetic energy.

Such change in speed defines a type of

energy storage referred to as the

Kinetic energy

is a non-negative scalar

quantity, meaning it has magnitude but

no direction. It has SI units of Joule.

kinetic energy of

the system

When work is done on a system and the only change in the system is in the speed of its

members, the net work done on the system equates to the change in the

defined part of the universe selected for analysis

In physics, a "system" refers to:

Energy transferred by a force acting through displacement

Work is defined as

• Negative

If the force and displacement are in opposite directions, the work done is

Scalar

The dot product of two vectors results in a

• Energy is transferred into the system

Positive work is done when:

• Gravity and normal force

Which forces do no work when an object moves horizontally?

• Positive

The work done by gravity on a free-falling object is:

It opposes the direction of motion

Friction does negative work because:

A force causes displacement

Work-energy transfer happens when:

When force is constant

When is the formula W = F . Ar valid?

20j

If a force vs. position graph shows a rectangle from 0 to 4 m at 5 N, the work is

Initial and final position

In the integral W = Sa: F(x) dx, the limits

represent:

F= -kx

Hooke's Law is given by:

Spring resists deformation by pulling or pushing opposite to x

In Hooke's Law, the negative sign means:

No spring force acts

If the spring is at its relaxed position (x = 0), then:

depends on deformation x

Spring force is a varying force because:

The force opposes the displacement

Work done by a spring is negative when:

Positive

The spring constant k is always:

Straight line

A graph of spring force vs. displacement is a:

Mass and velocity

Kinetic energy depends on which two quantities?

Its change in kinetic energy

According to the work-kinetic energy theorem, the net work done on an object is equal to:

Gravitational potential energy

Which quantity increases as an object is lifted vertically at constant speed?

The spring is fully compressed or stretched

The elastic potential energy is maximum when:

Kinetic energy

In an ideal spring system, when the spring is released, its potential energy converts into:

All forces are conservative

Mechanical energy is conserved when:

Work done by non-conservative forces

The change in mechanical energy equals:

Energy conservation including friction work

The speed of a block sliding down a rough incline is determined using:

Frictional force

Which force requires path information to compute the work done?

Zero

Work done by a conservative force in a closed path is: