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## Physics library

### Course: Physics library>Unit 7

Lesson 1: Rotational kinematics

# Relationship between angular velocity and speed

How angular velocity relates to speed. Created by Sal Khan.

## Want to join the conversation?

• when you push a heavy swinging door, why is the door harder to push open if you mistakenly push on the side closer to the hing?(as opposed to pushing on the door handle on the opposite side of the hinge) •  There are two way of looking at this. One has to do with the concepts of rotational motion which involve moment or moment of inertia. The other has to do with levers and work.

The easiest to explain is using the lever. You are probably familiar with a teeter-totter where you have a lever with a pivot point in the middle of the lever so that to lift 50Kg on on end takes 50kg of force on the other. If you move the pivot point to one side of the other the ration of weight(force) to balance it changes. The case of the door the pivot point it at one edge and the "weight" can be considered to be at the center of the door. The closer you are to the pivot point the harder you have to push. This comes from the amount of work that is required to move the door.

To swing the door from the closed position to fully open is the same regardless of where it is pushed, this comes from the conservation of energy. Work is defined as a force acting over a distance, if there is no movement there is no work. So if it takes X amount of work to open the door if you push on the side opposite the hinge it moves mich further than close to the hinge so since the amount of work will always be X the force will have to be greater near the hinge.

For example if a door requires 10 Nm (Newton meters the SI unit of work) to open and the edge opposite the hinge moves 2 meters when you open it it only takes a 5N force to open it but if the portion of the door near the hinge you push on moves only 0.1m then you need to use a force of 100N to open it.
• Is there a recommended order I should be watching these in (besides the order on the left of the screen)? I'm watching these to supplement a class I'm taking this term, so I am getting it, but there seems to be very little in the way of order, as the excellent series on Cryptogaphy had.
I found an iPhone application that has a bunch of KA videos that don't seem to be on the site (Introduction to Motion 1, introduction to Motion 2, etc); The App Store had reviews that indicated that these were old videos that had been taken off the main site? I know this is getting off topic, but I'm finding this non-The-Big-Bang-Theory type of Physics much more interesting than I expected to, so I wanna learn more about it. • As I already answered Femke a few questions down, it would help to watch "Intro to vectors and scalars" first off, to explain the terminology. (unless you already understand it) And then Acceleration and Balanced and Unbalanced forces, working to an explanation of motion, and then Newton's Laws. After that, you can start watching the many problem solving videos :)

It's good that you're interested in physics! There's a lot more to science than just cosmology and astronomy.
• How does angular velocity relate to linear velocity? • Linear velocity is speed in a straight line (measured in m/s) while angular velocity is the change in angle over time (measured in rad/s, which can be converted into degrees as well). Since the arclength around a circle is given by the radius*angle (l = r*theta), you can convert an angular velocity w into linear velocity v by multiplying it by the radius r, so v = rw.
• why is it that angular displacement is not a vector, whereas, an infinitely small angular displacement is a vector? • If you look at angular displacement as a whole,the direction keeps changing every millisecond or so ,since the path followed is curved.We can't do vector math with that.Now,imagine zooming in on the circumference of a circle.There will be a point where we have zoomed in so much that the part of the circumference we're looking at would look like a straight line.It's sorta what happens when we think roads are straight even though the surface of Earth is curved.This is what happens with infinitely small angular displacement.It can be considered a straight line,so it'll have a definite direction and will allow us to use it for vector math.
Hope that helps :)
• Why not just say 6.28 per seconds instead of 2pi? If there are 6.28 radians, 2pi*2pi, in a 360% circle, what is the purpose of saying 2pi? Maybe I'm just confused. • Angular velocity (w) = Radians (Angle covered) / second. At:5.53, it is written that Angular velocity = w Radians / second. Why did he add an 'w' there instead of simply writing Radians / second. • What is the difference between lower case omega and upper case omega? • At about ,Sal talks about the derivative of an angle.What does that mean?
(1 vote) • A circular turn table has a block of ice placed at it's centre.The system rotates with an angular speed omega(w) about an axis passing through the centre of the table.if the ice melts on it's own without any evaporation. What is the effect on the angular speed?
(1 vote) • Are the following motions are same or different ? and how ?
1. Motion of tip of second hand of a clock .
2. Motion of entire second hand of a clock .
(1 vote) 