Circular motion

  • #1
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.
 

Answers and Replies

  • #2
Doc Al
Mentor
45,011
1,288
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.
 
  • #3
ibc
82
0
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
 
  • #4
2,193
2
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. :eek:
 

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