Motion,moment of inertia,torque

SHOMITRO KUMAR GHOSH ID NO:161-15-7573 Daffodil International University

Newton’s law of Motion Friction Projectile motion Work & Energy Moment of inertia Torque & some mathematical

problems

MY TOPIC…

Newton's Three Laws of Motion

Newton's First Law of Motion:

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

Newton's Second Law of Motion:

The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma.

Newton's Second Law of Motion:

For every action there is an equal and opposite reaction.

Newton Third Law

Friction:

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction.

Friction:

Projectile Motion:

Projectile motion is a form of motion in which an object or particle called a projectile is thrown near the earth's surface, and it moves along a curved path under the action of gravity only.

The initial velocity

Projectile Motion:

Acceleration

Velocity

Displacement

,

Projectile Motion:

Total Flight time:

The total time t for which the projectile remains in the air is called the time of flight.

After the flight, the projectile returns to the horizontal axis, so y=0

Projectile Motion:

Maximum height of projectile

Maximum distance of projectile

Work & Energy:

Work

The work done by a constant force acting on an object is equal to the displacement times the component of the force parallel to that displacement.

Work & Energy:

Work & Energy:

EnergyEnergy is anything that can be con-verted into work; i.e., anything that can exert a force through a distance.

Energy is the capability for doing work.

The Work-Energy TheoremWork is equal to the change in ½mv2 If we define kinetic energy as ½mv2 then

we can state a very important physical principle:

The Work-Energy Theorem: The work done by a resultant force is equal to the change in kinetic energy that it produces.

2 21 102 2fWork mv mv

The Work-Energy Theorem

Moment of Inertia:

A measure of the resistance of a body to angular acceleration about a given axis that is equal to the sum of the products of each element of mass in the body and the square of the element's distance from the axis.

Mom

ent o

f Ine

rtia:

Moment of Inertia:

Solved Examples

Question 1: Calculate the Moment of inertia of the ball having mass of 5 Kg and radius of 3 cm?

Solution: Given: Mass of the ball = 5Kg,  Radius of the ball = 3 cm = 0.03 m,

Moment of Inertia is given by I = MR2                                             = 5 Kg × (0.03 m)2

                                            = 0.0045 Kgm2.

Moment of Inertia:

Solved Examples

Question 2: A sphere is moving around in air. If the moment of inertia is 10 Kgm2 and radius of 1m, Calculate its mass?

Solution: Moment of inertia I = 10 Kgm2,

Radius of sphere R = 1m,

Moment of Inertia I = MR2

Mass of the body M = I/R2 = 10/1 = 10 Kg.                                     

Torque:

Torque is a measure of how much a force acting on an object causes that object to rotate.

Torque:

Equation of torque

Torque: