# Circular motion and angular speed

In summary: There isn't a big difference between them, but angular velocity is usually used when talking about rotation in a specific direction (like around a circle). Angular acceleration is the rate of rotation, and tangential acceleration is the speed at a specific point (like at the point of collision). Centripetal force is the force that keeps an object moving in a circular direction.
http://www.hpcsoft.com/products/MathSoL/geom/cylinder.jpg

A cylinder is rotating with angular speed
-- take some points along radius and find if they have same angular speed ?
---- same tangential speed ?
------ same tangential acceleration ?

I think that they will have will same angular speed becuase all the points on the cylinder are moving with same speed.
But tangential speed would be different because it is the speed which is calculated at a specific point and each point will have different direction while moving.
and for tangential acceleration .. each point would have different.

Tell me if I am doing it right .
Thanks

You are correct about the angular speed; it is common to all points. The tangential speed is different for points that are different distances from the axis. Speed is not about direction. Speed is the magnitude of the velocity. All points along a given radius in the object are moving in the same direction but with different speeds. The same is true of the tangential acceleration. Tangential speed and acceleration are both proportional to the distance from the axis of rotation.

Thanks

what about the tangential veocity ... I think its the different as you told that the points at different distances would have different tangential velocity.
is it rite ?
I am very very confused about these terms :
angular speed, angular velocity, tangential speed, tangential velocity, tangential acceleration and angular acceleration.

I don't get that what's the main difference between them ? what do we spcifically look for ? (I mean distance from the axis or the angles, directions etc).
Please if someone can clear this . I'll be really thankful to you.

SPEEDS -- always magnitudes, never directions... but magnitudes might be dependent on position (esp. radius). Think about a row in a marching band rounding a corner but trying to keep in synch -- the guys on the ouside have FAST speeds but the guys on the inside scarcely move. (The Rose Bowl parade has one camera location particularly known for shooting this shot.)

VELOCITIES -- has the magnitude of the related speed but WITH directions.

ANGULAR means the motion is clockwise or counterclockwise. Think of two marching band lines marching at the same rate towards a corner. As they head towards a crash collision, each two band members at the same r have the same angular speed, the guys on the outside of the corner have the fastest speeds -- and the guys on the inside have the slowest. But since one band line is rounding one way, and the other the other way, the two guys at each r have different angular velocities. Interesting enough... once they start rounding the corner, the guys collide all at the same time at the same angle... isn't that kinda cool and unexpected? (Think of joining your hands at the wrist and slapping them together slowly (or fast)).

TANGENTIAL means tangential to the circle's arc. Think back to just one line rounding the corner, and the guy on the outside. Since he is changing direction as he moves around the radius, his tangential velocity is changing but since his motion is still in the same direction, his angular velocity is not.

ACCELERATION relates to a change in velocity. Even if an object's speed is not varying, if its direction is then there is an acceleration. So even if the angular velocity is constant, there is an acceleration. A centripetal acceleration (pointing in) is needed to keep an object in motion at a constant radius -- it pulls the object back in. If the rate of rotation is changing, then there is both an angular and tangential acceleration.

I found this series of interesting diagrams by googling: http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/RotationalKinematics/
and wikipedia's section on "centripetal force" might be useful too.

mini-edit for minor thngs

Last edited by a moderator:
Thanks a lot ... that's really helpful.

## 1. What is circular motion?

Circular motion is the movement of an object along a circular path. The object travels at a constant distance from a fixed point, known as the center of the circle.

## 2. How is angular speed different from linear speed?

Angular speed is the rate at which an object rotates around a fixed point, while linear speed is the rate at which an object moves in a straight line. Angular speed is measured in radians per second, while linear speed is measured in meters per second.

## 3. What factors affect the angular speed of an object?

The angular speed of an object is affected by the radius of the circular path, the time it takes to complete one rotation, and the mass of the object. It is also affected by any external forces acting on the object, such as friction or gravity.

## 4. How is angular speed related to angular velocity?

Angular velocity is a vector quantity that includes both the speed and direction of an object's rotation. Angular speed, on the other hand, only measures the magnitude of the rotation. The angular velocity is equal to the angular speed divided by the radius of the circular path.

## 5. What are some real-life examples of circular motion?

Some examples of circular motion in everyday life include the rotation of the Earth around the Sun, the motion of a Ferris wheel, and the spinning of a record on a turntable. Other examples include the motion of a satellite in orbit and the circular motion of a swinging pendulum.

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