Angular Acceleration vs Tangential Acceleration

Hey Telanor,

If the mass was fixed where represented by the point in your diagram, then the force will only produce angular accleration, as a constant force will produce acceleration around that point.

If the mass isn't fixed, the mass will exhibit both rotational and translational movement and acceleration.

 

Ok, lets keep things simple. Way more simple. Draw a line on the box. That line will rotate an angle theta as you apply the force. That angle will get bigger and biger as you keep on applying the force. The rate at which that angle gets bigger is the angluar velocity. Same deal for the angular acceleration.

NOW, each point on the body will have a DIFFERENT tangential velocity. It will depend on how far out it is-i.e. the radius. At the very center of rotation, the tangential velocity will be zero. As you move further out, it will increase. This is because it is proportional to radius.

Consider this. All points on the body are rigid. As it sweeps an angle, lets say theta, all the points rotate. But the points on the OUTTER most edge must sweep a BIGGER circle in the same amount of time, hence they must have a higher TANGENTIAL acceleration.