Difference between Linear speed and velocity and Angular speed and velocity?

Question

I mean I know what is the difference between linear and angular in the concept, but how do you differentiate the speed and velocity part. I know velocity has direction, so does that mean that Angular speed does not occur? and you should use angular velocity always?

Answer 1

I think you're confused because you're assuming that angular velocity and linear velocity have the same units.



As you know velocity has a direction, and its magnitude, speed, is in meters per second, so for example, for v= -2 m/s, the speed is 2 m/s, direction left, nothing new to you I'm sure. By convention left or down is negative, and up or right is positive. That said:



Angular velocity is a quantity measured in radians or degrees per second instead of m/s. And by convention, positive angular velocity means counter-clockwise when viewed from above and negative is clockwise, so I guess "direction" in angular velocity is counterclockwise or clockwise. So the magnitude, the speed, is in rad or deg/sec. For example, a top spinning at 360deg/s spins with a speed of 360 degrees every second, in the counterclockwise direction

Answer 2

The direction of angular velocity is probably your first introduction to a property of physics that is not intuitive. First let's look at angular speed: W (omega).



W = 2pi F; where F is the rotational frequency often given as rpm or cycles per second. W is in radians per unit time, usually seconds, as in radians per second. W is the angular speed, it has no direction just like linear speed has no direction. But like linear speed, we can add direction and convert angular speed into angular velocity. Here's how.



Angular momentum is L = I W; where I = kr^2 M is the moment of inertia of a mass M have radius of gyration r. k is a shape/mass specific number (e.g., 2/5 = k for a sold sphere).



Like linear momentum, P = MV, angular momentum has direction, but this is tricky because its direction is not aligned with the direction of motion. W is rotating; so it's continuously changing direction, but measures in the lab show that angular momentum is actually stable in one direction...perpendicular to the spinning direction. So, if you look down onto the top of a top and it's spinning in the CCW direction, the angular momentum vector, L, is pointing up towards you. By curling the fingers of your right hand in the direction of the spin, the extended thumb points in the direction of L. And that's why they call it the right hand rule.



As I in L = I W is a scalar, the direction of L comes solely from the direction of the angular velocity. So it's the spin of the top in the counter clockwise direction that makes the angular velocity vector point up and that aligns the angular momentum upward. It's this rather bizarre and totally non-intuitive direction of the momentum and underlying angular velocity that gives us the so-called gyroscopic effect.



And there you are. When concerned only with angular speed, W, we just plug and chug, as in L = I W = k mr^2 W. But when we need to include the direction of the W vector or the angular momentum vector L, then we must invoke the right hand rule to determine the direction of those vectors.



And, no, we don't always use W as a vector. In KE = 1/2 IW^2, which is kinetic energy due to angular motion, W^2 is a scalar, a speed, squared. Energy doesn't have a direction; force does, but not energy.

Answer 3

Angular speed has to do with how fast an angle is changing, or how fast an object is rotating. Angular velocity also specifies the "direction" of rotation, but the direction of the vector is defined differently from velocity. By convention, the vector is perpendicular to the plane of rotation and you use the right hand rule to know which 2 directions perpendicular to the plane the vector points. Angular speed is the magnitude of angular velocity.