Simple and quick question on rotational motions

SecretSnow

Hi guys, if a particle that is rotating around a axis at a constant angular acceleration, and at the highest point, it broke loose and flies off tangently and horizontally into the air, does it have a tangential acceleration of r*angular acceleration alpha? Please help!! This is found in University physics textbook qns 9.63 and the answer never includes the tangential acceleration although I think it should!

lewando

After the particle breaks loose, what forces are acting on it?

SecretSnow

I think it's weight...and nothing else? Oh!!! I see.... So the tangential acceleration serves its purpose only when it's rotating?

lewando

Yes.
"serves its purpose" is a little bit unclear. The particle, while attached to the accelerating wheel, experiences tangential acceleration and radial acceleration.

SecretSnow

Serves it purposes meaning speeding up the tangential velocity. So it only still speeds up the tangential velocity while spinning right? Thanks a lot!

lewando

Sorry, words are failing me lately. I would say that while the wheel is experiencing angular acceleration, the particle is experiencing tangential acceleration, with a resulting change in tangential velocity (could be speeding up or slowing down based on the direction of angular acceleration), as long as it is attached.

ehild

Any time a particle moves along a curved path we can speak about tangential and radial acceleration.
The tangential acceleration is along the tangent of the path, and its magnitude is a_t=dv/dt, derivative of the speed with respect to time. The radial acceleration is normal to the tangent and points toward the centre of the curvature of the path; the magnitude is v²/R where R is the radius of curvature.

When the particle loses contact, it experiences a different force as before: gravity instead of the resultant force which forced it move along the circle with constant angular acceleration. The acceleration is proportional to the force: the force changes so does the acceleration. At the same time the velocity stays the same as just before loosing the contact, it is horizontal.

As the force is vertical and the particle moves horizontally at the first instant after breaking loose, there is no tangential force acting on it so the tangential acceleration is zero.
Later on, the particle moves like a projectile along a parabola. With respect to that parabola, gravity has both tangential and radial components, so there will be both radial and tangential components of the acceleration.

ehild