I can realize that they are different, but can't understand what actually creates a rotational motion. Rotational motion doesn't mean just moving in a circle. There must be rotation of the position vector for rotational motion. For that, torque is required. Centripetal force,on the other hand,rotates the velocity vector. If this is the difference,what actually makes a door to rotate? Most book writes, it is torque, since the postition vector of the door's edge is rotating with respect to a hinge. But isn't there centripetal force,which is changing the direction of the velocity vector of the edge of the door to let it move in a circle?? What is actually happening? What is the difference between these two (apart from units!)??
Rotational Dynamics – What Causes a Door to Rotate: Torque or Centripetal Force?
rotational-dynamics
Related Solutions
In order to have a centripetal force, you must have mass that rotates around certain point. You should be more specific with your question, that is, you must tell us which mass is rotating and then we can tell you which centripetal force is responsible for that rotation.
Here is a more complete explanation on where does the centripetal force come from: Let's suppose we are standing in intertial frame of reference. As first Newton law states: if no force is exerted to a body, velocity of the body remains constant. Now what about rotating? In rotating velocity is not constant!
OK, velocity is vector, and it is possible that the body rotates in a way that the magnitude of the vector is constant. However, if the body is rotating, the direction of the vector of the velocity is changing! Therefore, some force must exert on the body, must force the body to rotate. It turns out that the force, that changes the direction of the vector of the velocity is directed toward the center of the rotation, and therefore we call that force centripetal force (petere in Latin means: to make for, tend to get to), i.e. force that tends toward center.
For specific explanation provide specific case.
Imagine two masses connected by a spring, like this:
If the entire thing spins at a constant angular velocity, the masses are moving in circles. Then $m_1$ and $m_2$ must have forces on them, since circular motion is a form of accelerated motion.
These forces are supplied by the spring. The spring will stretch somewhat, exerting forces pulling the masses back towards their equilibrium position. The magnitude of these forces is the usual centripetal force $m \omega^2 r$.
Now suppose you have a disk rotating like this:
The situation is very similar. If you take a point on this disk (besides the center), it's going in a circle. Therefore, this point has a centripetal acceleration, and must feel a force. Where is this force coming from?
The answer is that the force is coming from the disk itself. Imagine the disk as being a mesh of many points, all connected by springs. When you start the disk spinning, all the springs will stretch a little bit, exerting forces on the masses they're connected to. The net force of the springs on any given mass will be the centripetal force.
The way we usually express this is to say the entire disk is under tension (negative pressure). The tension decreases from a maximum at the center to zero at the edge. The gradient of the tension gives the force per unit volume, and that force is $\omega^2 r \rho \mathrm{d}V$ on a volume element $\mathrm{d}V$.
Best Answer
Centripetal force and torque are two very different things. Applying a torque to the door will cause angular acceleration while the centripetal force preserves rotation. The centripetal force is required to maintain circular motion and is provided by the bonds between the molecules in the door. A door is fairly rigid and so this force can be ignored as the "right amount" of centripetal force will be provided.
Your confusion is between torque and centripetal force. The torque produces the angular acceleration which changes the door's angular displacement, which causes the door to spin. The centripetal force, which is provided by the bonds between the molecules and in the hinge, keeps the door in its circular motion (otherwise the door would fly in a straight line).