Circular Motion: Perpendicular Force & Velocity Change Explained Quickly

[tasnim rahman]

A force on a moving object, in any direction other than direction of motion causes an overall change in velocity(both in magnitude and direction). Then in circular motion why does a perpendicular force applied change only direction and not magnitude. Is this because the force produces 0 velocity change towards the center at any instant, but overall circular velocity change? Someone please explain quickly.

 

[Doc Al]

Only a force with a component parallel to an object's velocity can cause a change in the magnitude of the velocity. In uniform circular motion, the force is always perpendicular to the velocity, so only the direction changes.

 

[ibc]

A force that is always perpendicular to the direction of motion does not change the magnitude of the velocity.

One way of seeing it is considering the energy a force insert to the system (or the energy per unit time):
P=\vec{f}*\vec{}v = 0

Another way is simply taking the derivative of the magnitude of the velocity (assume 2-D case):
d(v^2)\dt= d(v_x)^2\dt + d(v_y)^2\dt = 2(a_x*v_x + a_y*v_y) = 2\vec{a}*\vec{v}= 2\m(\vec{f}*\vec{v}) = 0

 

[pallidin]

A force that is always perpendicular to the direction of motion does not change the magnitude of the velocity.

One way of seeing it is considering the energy a force insert to the system (or the energy per unit time):
P=\vec{f}*\vec{}v = 0

Another way is simply taking the derivative of the magnitude of the velocity (assume 2-D case):
d(v^2)\dt= d(v_x)^2\dt + d(v_y)^2\dt = 2(a_x*v_x + a_y*v_y) = 2\vec{a}*\vec{v}= 2\m(\vec{f}*\vec{v}) = 0

I believe that should be perfectly clear to everyone.