If multiple forces are acting on the object such as, in your vertical example, gravity as well as the pull of a string then in general the tension force is not equal to the centripetal force, as it is only the net force the vector sum of all the forces that accelerates the object. What happens to velocity when radius increases? Is radius directly proportional to velocity? They show that 1 keeping radius constant implies that centripetal acceleration is proportional to the square of the velocity, 2 keeping velocity constant while varying the radius implies that centripetal acceleration is inversely proportional to the radius.
What is the formula of centrifugal force? How does radius affect circular motion? There are two possibilities: 1: The radius of circle is constant like in the motion along a circular rail or motor track. A change in v will change the magnitude of radial acceleration. This means that the centripetal acceleration is not constant, as is the case with uniform circular motion.
What happens to centripetal acceleration as radius increases? If you are keeping speed constant and increasing the radius then the centripetal acceleration would decrease. A bigger acceleration can result in two ways - either from a larger change in velocity, or from the velocity changing in a shorter amount of time. Why does centripetal force increase as radius decreases? If the curve is very sharp small radius , the object changes direction very quickly and for a given velocity Ac is higher.
Can you go around a curve with zero acceleration? The tangential and normal unit vectors at any given point on the curve provide a frame of reference at that point. Note that the centripetal force is proportional to the square of the velocity, implying that a doubling of speed will require four times the centripetal force to keep the motion in a circle.
The actual acceleration rate is dependent upon how rapidly the direction is being change and is directly related to the speed and inversely related to the radius of the turn. Accelerating an object can change both in the magnitude and direction of the velocity. Begin typing your search term above and press enter to search. Press ESC to cancel. Skip to content Home Physics What happens to centripetal acceleration when radius is doubled? Ben Davis August 3, Because if they aren't, all parameters might change simultaneously.
And when there is more than one parameter, anything can be said and nothing is known for sure because many setups of these parameters can make it work. So, be aware of the situation and the conditions. The statements that you refer too, require this knowledge - otherwise they are useless.
For any two situations where an object is in circular motion, assuming the linear velocity is equal in both cases, a larger radius requires less centripetal force to keep that object moving in the circle.
Perhaps an everyday example of this is driving on a highway curve. When you drive around a curve, you feel an "inertial" or "fictitious" centrifugal force, which feels stronger when you have more centripetal acceleration. So if you go around a curve of a small curvature - and therefore small radius - you feel like you are about to be thrown out of the car the fictitious force , which means you have a stronger centripetal acceleration.
However, if you drove at the same speed around a larger-radius curve, then you would not feel as much as much inertial force, and therefore the centripetal acceleration would be smaller. While you are changing the radius, you are not moving in a circle around the original center point. You are moving in a spiral of some kind. Think about a stone tied to a string being whirled in a circle.
If you pull harder on the string to shorten it, the stone starts to spiral inwards, and the string is applying a tangential force to the stone as well as the radial force that causes the centripetal acceleration. The tangential force will increase the speed of the stone around the circle as the radius decreases.
So there are two changes which have opposite effects on the tension in the string. Reducing the radius and keeping everything else the same would reduce the centripetal acceleration, but increasing the speed and keeping everything else the same would increase it.
To find out which effect "wins" you need to do some math, but you said you don't want a "formula". Also the question says "you" are moving in a circle, but it doesn't say how the centripetal force that keeps you moving in a circle is being applied to you.
So, you haven't fully described what the real-world system is, and you don't want to use the best way math to model how it behaves. Therefore, this isn't a complete answer!
There is a tension in the string because the ball is travelling in a circular motion. The tension force is constantly causing the ball to accelerate toward your fingers. The ball, at all times, wants to travel in a tangentially straight line away from your hand.
The tension is constantly preventing this from happening. The tension is related to 3 things; the mass of the ball, the velocity of the ball, and the radius of the string. If you increase the mass of the ball, the tension will increase to keep it in orbit at its present velocity and radius because more force is require to restrain the greater mass in the existing orbit. If you increase the radius of orbit and keep the velocity and mass the same, then the orbit is a larger and gentler curve.
You could increase the radius so much that the curve would be VERY gentle and theoretically approach the tangential line the ball truly wants to follow. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?
0コメント