why is an object in uniform circular motion expereincing centripetal acceleration ?

Think about Newton's first law: An object in motion will stay in motion at a constant speed in a straight line unless acted on upon by an outside force. An object that is moving has inertia that causes it to want to stay in motion in a straight line. But if an object is moving in a circle, the velocity is no longer in a straight line. This means that a force must be acting on the object which means that the object must be accelerating. It is this acceleration that we refer to as centripetal acceleration.

Is angular velocity only related with circular motion?

angular velocity must exist wherever angular displacement occurs, irrespective of shape of the path.

Why is angular velocity sometimes expresed in revolutions per minute, isn't that frecuency?

well, the angular velocity is expressed by the angular displacement over the change in time, so in your case the revolutions would be the angular displacement converted to revolutions, and the time would be in minutes. Although it isn't in the rad/s form, I suppose it is still the angular displacement per time (in minutes).

how to calculate angel velocity

Angel velocity is more of a theology subject than a physics subject C: But if you want to find _angular_ velocity, simply divide the angle traveled in radians by the time it took to rotate at that angle. The general equation is as follows: ω = (θ/t) where omega (ω) is in radians per seconds, theta (θ) is in radians, and t is in seconds.

what is a matching band

A marching band is a group of people playing musical instruments while walking/marching. Typically they wear uniforms and play their music in parades or at events.

i need 3 examples of circular motion please help me!!

The orbit of the moon is close. Twirling an object at the end of a string. Race cars driving in a circle. Roller coaster going in a loop.

To move a body in a circle which of th following forces in neend

For an object to be moving in circular motion, there has to be a net force towards the centre of the circle as the acceleration is towards the centre of the circle.

Main content

Course: AP®︎/College Physics 1 > Unit 4

Lesson 1: Uniform circular motion introduction

Uniform circular motion and centripetal acceleration review

Google Classroom

Review the key concepts, equations, and skills for uniform circular motion, including centripetal acceleration and the difference between linear and angular velocity.

Key terms

Term (symbol)	Meaning
Uniform circular motion	Motion in a circle at a constant speed
Radian	Ratio of an arc’s length to its radius. There are $2 π$ ‍ radians in a $360 °$ ‍ circle or one revolution. Unitless.
Angular velocity ( $ω$ ‍)	Measure of how an angle changes over time. The rotational analogue of linear velocity. Vector quantity with counterclockwise defined as the positive direction. SI units of $\frac{radians}{s}$ ‍.
Centripetal acceleration ( $a_{c}$ ‍)	Acceleration pointed towards the center of a curved path and perpendicular to the object’s velocity. Causes an object to change its direction and not its speed along a circular pathway. Also called radial acceleration. SI units are $\frac{m}{s^{2}}$ ‍.
Period ( $T$ ‍)	Time needed for one revolution. Inversely proportional to frequency. SI units of $s$ ‍.
Frequency ( $f$ ‍)	Number of revolutions per second for a rotating object. SI units of $\frac{1}{s}$ ‍ or $Hertz (Hz)$ ‍.

Equations

Equation	Symbol breakdown	Meaning in words
$Δ θ = \frac{Δ s}{r}$ ‍	$Δ θ$ ‍ is the rotation angle, $Δ s$ ‍ is the distance traveled around a circle, and $r$ ‍ is radius	The change in angle (in radians) is the ratio of distance travelled around the circle to the circle’s radius.
$\bar{ω} = \frac{Δ θ}{Δ t}$ ‍	$\bar{ω}$ ‍ is the average angular velocity, $Δ θ$ ‍ is rotation angle, and $Δ t$ ‍ is change in time	Average angular velocity is proportional to angular displacement and inversely proportional to time.
$v = r ω$ ‍	$v$ ‍ is linear speed, $r$ ‍ is radius, $ω$ ‍ is angular speed.	Linear speed is proportional to angular speed times radius $r$ ‍. Angular speed is the magnitude of the angular velocity.
$T = \frac{2 π}{ω} = \frac{1}{f}$ ‍	$T$ ‍ is period, $ω$ ‍ is angular speed, and $f$ ‍ is frequency	Period is inversely proportional to angular speed times a factor of $2 π$ ‍, and inversely proportional to frequency.

How to relate angular speed and linear speed

Angular velocity

ω

measures the amount of rotation per time. It is a vector and has a direction which corresponds to counterclockwise or clockwise motion (Figure 1).

Technically speaking counterclockwise is not a vector direction since a vector must point in a single direction. However, counterclockwise motion can correspond to a single vector direction. Mathematicians consider counterclockwise motion to correspond to the vector that points out of the page/screen. This is called the "right hand rule" since if you give a "thumbs up" with your right hand, your thumb points out of the counterclockwise swirl of your fingers.

That said, you can deal with most situations by simply associating counterclockwise motion with a positive angular velocity, and clockwise rotation with a negative angular velocity.

The same letter

ω

is often used to the represent the angular speed, which is the magnitude of the angular velocity.

Velocity

v

measures the amount of displacement per time. It is a vector and has a direction (Figure 1).

The same letter

v

is often used to represent the speed (sometimes called linear speed in these contexts to differentiate it from angular speed), which is the magnitude of the velocity.

The relationship between the speed

v

and the angular speed

ω

is given by the relationship

v = r ω

Angular speed does not change with radius

Angular speed

ω

does not change with radius, but linear speed

v

does. For example, in a marching band line going around a corner, the person on the outside has to take the largest steps to keep in line with everyone else. Therefore, the outside person who travels a greater distance per time, has a greater linear speed than the person closest to the inside. However, the angular speed of every person in the line is the same because they are moving through the same angle in the same amount of time (Figure 2).

Learn more

To check your understanding and work toward mastering these concepts, check out our exercise on calculating angular velocity, period, and frequency.

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aisha
Posted 4 years ago. Direct link to aisha's post “why is an object in unifo...”
why is an object in uniform circular motion expereincing centripetal acceleration ?
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(4 votes)
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- obiwan kenobi
  Posted 4 years ago. Direct link to obiwan kenobi's post “Think about Newton's firs...”
  Think about Newton's first law: An object in motion will stay in motion at a constant speed in a straight line unless acted on upon by an outside force. An object that is moving has inertia that causes it to want to stay in motion in a straight line. But if an object is moving in a circle, the velocity is no longer in a straight line. This means that a force must be acting on the object which means that the object must be accelerating. It is this acceleration that we refer to as centripetal acceleration.
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  (11 votes)
abkhanayan.02
Posted 5 years ago. Direct link to abkhanayan.02's post “Is angular velocity only ...”
Is angular velocity only related with circular motion?
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(4 votes)
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- Shikha
  Posted 3 years ago. Direct link to Shikha's post “angular velocity must exi...”
  angular velocity must exist wherever angular displacement occurs, irrespective of shape of the path.
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  (3 votes)
Milton Jimenez
Posted 4 years ago. Direct link to Milton Jimenez's post “Why is angular velocity s...”
Why is angular velocity sometimes expresed in revolutions per minute, isn't that frecuency?
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(4 votes)
Answer
- Le, Donna
  Posted 4 years ago. Direct link to Le, Donna's post “well, the angular velocit...”
  well, the angular velocity is expressed by the angular displacement over the change in time, so in your case the revolutions would be the angular displacement converted to revolutions, and the time would be in minutes. Although it isn't in the rad/s form, I suppose it is still the angular displacement per time (in minutes).
  Button navigates to signup page
  (2 votes)
manase0322
Posted 4 years ago. Direct link to manase0322's post “how to calculate angel ve...”
how to calculate angel velocity
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(1 vote)
Answer
- BeeGee
  Posted 4 years ago. Direct link to BeeGee's post “Angel velocity is more of...”
  Angel velocity is more of a theology subject than a physics subject C:
  But if you want to find angular velocity, simply divide the angle traveled in radians by the time it took to rotate at that angle.
  The general equation is as follows: ω = (θ/t) where omega (ω) is in radians per seconds, theta (θ) is in radians, and t is in seconds.
  Button navigates to signup page
  (7 votes)
maxou27
Posted 3 years ago. Direct link to maxou27's post “what is a matching band”
what is a matching band
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(1 vote)
Answer
- James Adams
  Posted 3 years ago. Direct link to James Adams's post “A marching band is a grou...”
  A marching band is a group of people playing musical instruments while walking/marching. Typically they wear uniforms and play their music in parades or at events.
  Comment on James Adams's post “A marching band is a grou...”
  (5 votes)
😊
Posted 6 years ago. Direct link to 😊's post “i need 3 examples of circ...”
i need 3 examples of circular motion please help me!!
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(0 votes)
Answer
- itpc932874
  Posted 6 years ago. Direct link to itpc932874's post “The orbit of the moon is ...”
  The orbit of the moon is close. Twirling an object at the end of a string. Race cars driving in a circle. Roller coaster going in a loop.
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  (10 votes)
Jonathan Alejos
Posted 3 years ago. Direct link to Jonathan Alejos's post “if you divide velocity (m...”
if you divide velocity (m/s) by the radius (m) you get the angular velocity which is measured (rad/s), is that right ?

(m/s) / (m) = rad/s ?
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(2 votes)
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- Katie.jt.louie
  Posted 3 years ago. Direct link to Katie.jt.louie's post “Yes, that is correct! Rad...”
  Yes, that is correct! Rads are units to express the central angle
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  (1 vote)
Bhavashruthi Mylsamy
Posted a year ago. Direct link to Bhavashruthi Mylsamy's post “isn't v= *cross product* ...”
isn't v= cross product of r and w?? then why is v given as speed instead of velocity??
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(2 votes)
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manisharawlani8423
Posted 6 years ago. Direct link to manisharawlani8423's post “To move a body in a cir...”
To move a body in a circle which of th following forces in neend
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(0 votes)
Answer
- Marcus
  Posted 5 years ago. Direct link to Marcus's post “For an object to be movin...”
  For an object to be moving in circular motion, there has to be a net force towards the centre of the circle as the acceleration is towards the centre of the circle.
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  (3 votes)
Винсент
Posted 3 years ago. Direct link to Винсент's post “I feel weird about the se...”
I feel weird about the sentence "The same letter omega is often used to the represent the angular speed, which is the magnitude of the angular velocity.".
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(1 vote)
Answer
- onetwothree
  Posted 2 years ago. Direct link to onetwothree's post “The same letter is used, ...”
  The same letter is used, but angular velocity is a vector quantity - ie: it has a direction AND a magnitude - and it is denoted by omega with a vector sign on top, while angular speed is a scalar quantity - ie: it only has a magnitude, and it is denoted with no sign on top. Since in the case of angular measures, the only direction is +ve or -ve, in effect angular speed is the absolute value of angular velocity. Hope this helps....
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  (1 vote)