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=[tex]\vec{f}[/tex]*[tex]\vec{}v[/tex] = 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[tex]\vec{a}[/tex]*[tex]\vec{v}[/tex]= 2\m([tex]\vec{f}[/tex]*[tex]\vec{v}[/tex]) = 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=[tex]\vec{f}[/tex]*[tex]\vec{}v[/tex] = 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[tex]\vec{a}[/tex]*[tex]\vec{v}[/tex]= 2\m([tex]\vec{f}[/tex]*[tex]\vec{v}[/tex]) = 0

I believe that should be perfectly clear to everyone.

 

[PJC01]

This is because in circular motion, the object is constantly changing direction, but its speed remains constant. This is due to the centripetal force, which is always directed towards the center of the circle and does not contribute to any change in speed. Therefore, when a perpendicular force is applied, it only affects the direction of the object's velocity, not its magnitude. This is because the perpendicular force is not acting in the direction of motion, so it does not contribute to any change in speed. Overall, the circular motion is maintained due to the balance between the centripetal force and the object's inertia.