Why a body moving in circle has acceleration perpendicular to velocity?

Question

By the motion of the body we consider its direction.
A body moving towards north with increasing velocity has both directions of velocity and acceleration towards north.
But when a body moves in circle ,acceleration becomes perpendicular to velocity and right hand rule becomes affective.
But why right hand rule is affective when there is no movement in perpendicular direction.

Answer 1

Suppose you are moving in a circle at constant speed s. Let v(t) be the vector-valued function which is the velocity at time t. Then = s^2. Here <,> denote the dot product operation. Taking the derivative of both sides and applying the product rule for dot products, we get 2 = 0. Therefore, the acceleration v'(t) is perpendicular to the velocity v(t).

Answer 2

Picture this experiment. You tie a rock to a string and start to swing it around above your head. As long as you hold the string tight the rock keeps going in a circle around you (for this just assume it is moving in a perfect circle). If you were to let go of the string the rock would go of in a straight line in some direction. So, there must be something that is keeping it from always going off in a straight line. So, at each point in the circle, there is a force that is pulling it towards the center.

Now is when vectors become useful in this experiment. You may find it helpful to draw this picture. Draw a circle. Now, pick any point you want on the circle. Draw a tangent line to this point. This is the direction that the stone will continue to go in if you were to let go of the string. This is also called the velocity vector. Now, since we already determined there is some force that is always pulling the stone towards the center, draw a line from the point to the center of the circle. This is the acceleration vector. Notice anything about these two vectors? Put the corner of a piece of paper to where these two lines meet and you should have an almost perfect right angle.

I'm not sure exactly what your question is about the right hand rule. It is always in effect. But it is only used by convention. It could just have easily been called the left hand rule.

Answer 3

Suppose the velocity is in the North direction and acceleration is toward East.

The body will move in a circular path in a clockwise direction.

If the acceleration is toward west, then the body will move in clockwise direction.

Thus we see in circular motion, we are having two directions a clockwise and anticlockwise.

The right hand screw rule is to determine the direction of rotation of bodies acted on by two directions which are inclined to each other.

Answer 4

by technique of definition, one you may study, acceleration A = dV/dT, is the substitute in speed over your time period. As speed is a vector having both value (speed) and route, dV will be <> 0 if the route is replacing even in spite of the undeniable fact that the speed isn't. as an example, in orbit, a satellite tv for pc could have a consistent tangential speed, yet because it truly is getting in a circle, it truly is route is often replacing. And that yields a radial acceleration of Ar = V^2/R the position V is the tangential speed and R is the orbital radius. Ar factors outward alongside the radius R. it truly is this radial acceleration, at the same time as more beneficial by technique of the mass, m, of the satellite tv for pc that provides us the centrifugal stress Fc = m Ar = m V^2/R. BTW. Ar factors outward. Ap is the acceleration that factors inward because of the centripetal stress it extremely is popping the article round an axis of rotation,. Centrifugal stress is a reaction stress to the real centripetal stress it is actual causing the orbiter to modify instructions. Centripetal stress for an orbiter is the stress of gravity.

Answer 5

All I know is that if you have constant velocity then there is 0 acceleration. Other than that I am too tired to answer this question.

Answer 6

the acceleration of a body in circular motion is directed towards its centre since it has only normal components no tangential ones. also its velocity has only tangential components no normal ones.as a tangent is always perpendicular to the radius,the acceleration is perpendicular to the velocity.
thats what i think...................

Answer 7

when the body moves in a circle, it has a tendency to move into the center of the circle, which makes it have a acceleration perpendicular to velocity