Uniformly Changing Circular Motion: Definition, Physical Quantities, Formulas and Examples of Problems

Uniformly Changing Circular Motion: Definition, Physical Quantities, Formulas and Examples of Problems – What is Uniformly Changed Circular Motion And Examples?, At this opportunity About the knowledge.co.id will discuss it and of course about other things that also cover it. Let's look at the discussion together in the article below to better understand it.

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Uniformly Changing Circular Motion: Definition, Physical Quantities, Formulas and Examples of Problems

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Circular motion is the motion of an object that forms a circular path around a fixed point. In order for an object to move in a circle, it needs a force that always deflects it towards the center of the circular path.

This force is called the centripetal force. A uniform circular motion can be said to be a uniformly accelerated motion, bearing in mind that there needs to be a acceleration of a fixed magnitude with a changing direction, which always changes the direction of motion of the object so that it takes a shaped trajectory circle

Uniform circular motion is a motion whose trajectory is in the form of a circle with a constant speed and the direction of velocity is perpendicular to the direction of acceleration. The direction of velocity continues to change while the object moves in the circle, as shown in the image above.

Since acceleration is defined as the magnitude of the change in velocity, a change in the direction of velocity results in acceleration as does a change in magnitude. Thus, an object traveling in a circle continues to accelerate, even when its speed remains constant (v1= v2= v).

Uniformly Changing Circular Motion (GMBB) is a circular motion with a constant angular acceleration. In this motion there is a tangential acceleration (which in this case is the same as the linear acceleration) which alludes to the circular path (coincides with the direction of the tangential velocity).

If the angular velocity increases, then there is an increase in velocity (acceleration) so that the angular acceleration is positive (α = +) which is also known as GMBB is accelerated, whereas if the blade speed decreases, there will be a reduction in speed (deceleration) so that the angular acceleration is negative (α = -) which is also known as GMBB slowed down.

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Characteristics of Uniformly Changed Circular Motion (GMBB)

• The track is a circle
• The motion of objects is influenced by centripetal force
• There is a change in the angular velocity of the object
• The angular acceleration is constant

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Physical quantities

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  Corner

Angle is a quantity in the form of a line segment from one starting point between one position to another. The international unit for angle is the radian (rad), but the more commonly used unit to describe angles is the degree.

A circle has an angle of 360 degrees. The symbol used to represent angles is theta (θ).

Formula :

1 Circle = 2phiradians = 360°

1 Radian = 360/2o

So

1 Radian = 180/degree

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• Angular Speed ​​and Linear Speed

  • Angular Speed ​​(Angular Speed)

Angular speed or what is also often referred to as angular speed is the angle traveled by a point moving on the edge of a circle in a certain time unit (t).

The international unit for angular speed is the rad per second (rad/s). The symbol used to represent angular velocity is omega (Ω or ω).

Formula :

ω = v/r

• • Linear Speed ​​(Tangential Speed)

Linear Velocity (Tangential Velocity) is a quantity in physics that shows how fast an object moves from one place to another.

The international unit used for linear speed is meters per second (m/s), but in everyday life it is in In Indonesia, of course we use kilometers per hour (km/hour) more often, while in America we use miles per hour more often. (mile/hour).

Speed ​​can be obtained by multiplying the distance traveled by the time traveled. The symbol for speed is v (lowercase).

Formula :

v = ω. r

Information :

• ω: Angular speed (rad/s)
• v: Linear speed (m/s)
• r: Radius(m)

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• Angular Acceleration and Linear Acceleration

  • Angular Acceleration (Angular Acceleration)

Angular acceleration is a change in angular velocity in a certain unit of time (t). If the angular velocity increases, there will be an angular acceleration (increase in speed) so that the angular acceleration is positive.

Meanwhile, if the angular velocity decreases, there will be a deceleration (speed reduction) so that the angular acceleration is negative.

The international unit for angular acceleration is radians per second squared (rad/s²). The symbol used to represent angular acceleration is alpha (α).

Formula :

α = Δω / Δt

• Linear Acceleration (Tangential Acceleration)

Linear acceleration or tangential acceleration is a change in velocity that occurs to the object, either due to the influence of a force acting on the object or because of the state of the object. The international unit for speed is m/s² .

The symbol used to represent linear acceleration is "a". If the change in velocity is negative (the object's speed decreases) then it is called deceleration (a = -), whereas if the change in velocity is positive (speed increases) then it is called acceleration (a = +).

Formula :

a = ω². r

or

a = v² / r

Information :

• α: Angular acceleration (rad/s²)
• a: Linear acceleration (rad/s²)
• ω: Angular speed (rad/s)
• v: Linear speed (m/s)
• r: Radius(m)

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• Traveling time

Travel time is the time needed by an object to move from one position to another at a certain speed. The International Unit for Travel Time is second(s).

While the symbol used to represent the travel time is t (lowercase). Travel time can be obtained by dividing the distance by the speed.

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• Frequency and Period

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    Frequency

In general, frequency is a measure of the number of repetitions of an event in a certain time. In circular motion, frequency is the number of revolutions an object can make in one second.

The international unit used for frequency is Hertz (Hz). The symbol used to represent frequency is f (lowercase).

Formula :

T=1/f

T=t/n

• • Period

In general, the period is the time taken to carry out an event. In circular motion, the period is the time it takes to complete one circle.

The unit often used for the period is the second or second(s). The symbol used to represent the period is T (uppercase).

Formula :

f = 1/T

f=n/t

Information :

• Q: Period(s)
• f: Frequency (Hz)
• t: Time(s)
• n: Number of Loops

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• Radius

The radius or what we also often call the radius of a circle is the line that connects the center point to the outermost part of a circle.

The units that are often used for radius are units of length such as meters (m), centimeters (cm), kilometers (km), etc. The symbol used to represent the radius is r (lowercase).

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Uniformly Changed Circular Motion Formula (GMBB)

ωo = ωt ± α. t

(ωo) ² = (ωt) ² ± 2. α. t

θ = ωo. t ± ½ α. t

Information :

• θ: Angle (rad)
• ωo: Initial angular velocity (rad/s)
• ωt: Final angular velocity (rad/s)
• t: Time(s)
• α: Angular acceleration (rad/s)

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Examples of Uniformly Changing Circular Motion Questions (GMBB)

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Problem 1:

An object makes circular motion with a constant angular speed of 0.5π rad/s. Calculate how many rotations the object produces in one minute?

Discussion :

Is known :

ω = 0.5π rad/s

asked :

f ?

Answer :

ω = 2πf

f = ω/2π

= 0,5π / 2π

= 4 Hz

So, The result of rotating objects in one minute is 4 Hz

Example 1 :

A grinding wheel rotates from rest with an angular acceleration of 3.2 rad/s². Define:

1. The angular displacement experienced by a point on the grinding wheel after 2 seconds?
2. What is the angular velocity of the grinding wheel after 2 seconds?

Answer :

1. ɵ = ω_o .t + ½ α .t²

= 0.2 + ½.3,2. 2²

= 6.4 radians

1. ω_t = ω_o + α. t

= 0 + 3,2. 2 = 6.4 rad/s

Problem 2:

An electric fan is rotating. When the angular speed is 9.6 rad/s, the fan is turned off, so the fan's movement is slowed down with a fixed angle deceleration, finally the fan stops after 192 seconds. Define:

1. Angular acceleration?
2. The linear distance traveled by the tip of the fan radius from when the fan is turned off, until it stops, if the radius of the fan is 20 cm?

Answer :

1. α = ω_t – ω_o

t

= 0 – 9,6

192

= – 0.05 rad/s²

The negative sign means a reduction in speed or a deceleration occurs.

1. ɵ = ω_o .t + ½.α .t²

= 9,6. 192 + ½.-0,05.192²

= 1843,2 – 921,6

= 921.6 radians

So,

S = r. ɵ

= 20. 921.6 = 18432 meters

Question 3 :

An object rotating with a speed of 5 rad/s travels an angle of 40 radians in 3 seconds, how much angular acceleration is needed:

Answer :

Because the problem is known the travel angle, the formula used is:

ɵ = ω_o .t + ½ α .t²

40 = 5. 3 + ½ α.3²

40 = 15 + 4,5α

40 – 15 = 4,5α

25/4,5 = α

5.6 rad/s² = α

Question 4 :

A train passes through a circular track with an initial angular velocity of 10 rad/s and an angular acceleration of 5 rad/s². The time it takes for the initial angular velocity to reach the final angular velocity is 5 seconds. Define:

1. The angular acceleration at t = 3 seconds?
2. The angular displacement at t = 3 seconds ?

Answer :

1. ω_t = ω_o + α. t

= 10 + 5.3 = 25 rad/s

1. ɵ = ω_o .t + ½.α .t²

= 10.3 + ½.5.3²

= 30 + 22.5 = 52.5 radians

Question 5 :

An object rotates with an angular speed of 3 rad/s. If after 6 seconds the object stops moving. Define:

1. Angular acceleration?
2. The angle of travel?

Answer :

Is known :

ω_t = 0

ω_o = 3 rad/s

t = 6 seconds

1. ω_t = ω_o – α. t

• = 3 – α. 6

α 6 = 3

α = 3/6 = 0.5 rad/s²

1. ω_t² = ω_o² – 2. α. ɵ

0² = 3² – 2.0,5. ɵ

0 = 9 – 1. ɵ

1ɵ = 9

ɵ = 9/1 = 9 radians

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