CIRCULAR

MOTION

• CRSHS, III- Galileo, Physics

Teacher: Mrs. Maria Ruth Edradan

Group 4 task:Catulay powerpointYee laptopPomoy infoMatildo infoBonono infoJoaquino questions

• SIGNIFICANCE OF CIRCULAR MOTION

Uniform circular motion helps you in

understanding the various principles of

physics. 

1. Centripetal and centrifugal forces

2. Motion of electrons in an atom

3. Earth's structure and concept of its

gravity

4. Various mechanical devices like merry go

round, etc.

5. Understanding various laws of physics

Motion in a Circle

The rules of circular motion help us to describe:• movement of a car going round a corner,• a tethered model aeroplane;• the planets in their orbits.

Angular Velocity

• The speed of a body moving in a circle can be specified either by its speed along the tangent at any instant (linear speed) or by the angular

velocity. This is the angle swept out in unit time by the radius joining the body to the

centre. It is measured in [rad s-1].

Angular Acceleration• Angular acceleration is the rate of

change of angular velocity over time. In SI units, it is measured in radians per second squared(㎯， rad/s2), and is usually denoted by the Greek letter alpha (α).

Mathematical definition• The angular acceleration can be defined as

either:

• where ω is the angular velocity, aT is the linear tangential acceleration, and r is the distance from the origin of the coordinate system that defines θ and ω to the point of interest.

Angular Acceleration

Linear Acceleration

• The linear acceleration of a body is the rate of change of linear velocity with time. It is a vector.

• If acceleration is uniform the speed must be increasing by equal amount in equal time intervals.

CIRCULAR MOTION: introduction

In physics, circular motion is rotation along a circle: a circular path or a circular orbit.

It can be uniform, that is, with constant angular rate of rotation, or non-uniform, that is, with a changing rate of rotation.

Circular motion is another simple type of motion. If an object has constant speed but an acceleration always at right angles to its velocity, it will travel in a circle. The required acceleration is directed toward the center of the circle and is called centripetal acceleration .

CIRCULAR MOTION: introduction

• Centripetal acceleration-

acceleration that

maintains the object

along a circular path,

directed towards the

center.

Uniform Circular Motion

UNIFORM CIRCULAR MOTION

An object moves at a constant speed along a circular path.

Uniform Circular Motion• Uniform circular motion can be

described as the motion of an object in a circle at a constant speed.

• As an object moves in a circle, it is constantly changing its direction.

• At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well.

Speed Vs. Velocity• If the speed is constant, will the

velocity be constant? _______________________________• Why is velocity not constant?_______________________________

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Centripetal Acceleration• In 1673, Christian Huygens was able to determine the following relationship

between ac, v and R.

• Changing velocity is acceleration. The acceleration of the object is directed toward the center of the circle, and is of constant magnitude a=v2/r, where r is the radius of the circle and v is the speed of the object (with mass m). This type of acceleration is called radial or centripetal acceleration.

• Radial acceleration results from the action of the force generated by the string that pulls the ball toward the center of the circle. In the case of a satellite in orbit, the force causing the radial acceleration is Earth’s gravity pulling the satellite toward the center of the planet.

ac=V2 /R

Centripetal Acceleration

• A ball on the end of a string being whirled overhead at a constant speed is an example of this type of acceleration.

• Since velocity is a vector quantity like acceleration, velocity has a speed component (magnitude) and a direction component.

• At every instant in its motion overhead, the ball’s velocity is changing because the velocity’s direction is different at every point on the circular path.

Acceleration can also involve a change in the direction an object is moving

• When a body goes around the circle of radius r, it is just travelling around the circumference of the circle, so it covers the entire distance equivalent to 2∏r. Instead of using time, we introduce a new term, called Period,

represented by the Greek letter tau (T)So, velocity is equivalent to the following formula:

Instead of measuring the time it takes to complete one revolution, you could also identify time in terms of the number of revolution of cycle completed per unit time. This term is called frequency, represented by the letter f.Frequency and Period are related by this equation:

f= 1/T

It can also be expressed in terms of frequency:

v= 2∏rf

Expressing our centripetal acceleration in terms of frequency:

∏∏

In terms of period:

Examples

It takes a merry-go-round

moves 30 seconds to complete

one revolution, what is the

velocity of the child on top of a

horse found 3.0 m away from

the center?

A micro compact disc (CD) is 6.0

cm in diameter. If a Drive spins

uniformly at 300 revolutions per

minute, what is the acceleration

in m/s2 of a particle of dirt found

along the edge.?