What is the formula to get the angle of banking in uniform circular motion?

Answer 1

tan(theta) =( velocity^2/radius*acceleration due to gravity)
theta = angle of banking.......

Answer 2

Uniform circular motion is defined as motion at a constant speed following a circular path.

The period of an object in uniform circular motion is the time required for the object to complete the path one time.

The equation relating period and speed is:


V = 2ΠR/T


Where V = speed, r = radius of circle, and T = period.

The units for T will be seconds or minutes per revolution.

Remember, although the speed is constant, the velocity is not since the direction is always changing.

Centripetal acceleration is the name for acceleration that is always at a right angle to the velocity vector direction causing the object to move in a circular path.

The magnitude pf centripetal acceleration can be found using the formula:


Ac = V2/R


Where Ac = centripetal acceleration, V = speed, and R = radius of the circle. It is helpful to remember that the velocity vector is always oriented tangent to the circular path. This causes the velocity to be oriented perpendicular to both the radius of the circle and the centripetal acceleration which is in the same direction as the radius.


From the equation above we can see that the centripetal acceleration depends directly on the square of the speed of the object and inversely on the radius of the circular motion. In other words, more speed produces a larger acceleration, but a larger radius produces a smaller acceleration.

Answer 3

The magnitude of the acceleration is given by a = v2 / r, where v is the speed of the object and r is the radius of its path, or a = (4π2r) / t2, where r is the radius of the object and t is the time it takes the object to travel a distance.


Initial velocity = v1, Final velocity= v2, a = acceleration, r = radius of circular path, s = sector traveled

We follow the head-tail rule for adding vectors. Since the initial velocity points in the opposite direction as it is drawn on the circle diagram, we label it - v1. Thus getting the equation: v2-v1

a = (v2-v1) / t

a = (v2-v1) / t

at = |v2-v1| We use the absolute value of v2-v1 because we only focus on the magnitude of the velocity.

At this point we can set up a proportion: |v2-v1| / v = s / r

We substitute at for |v2-v1|, which gets us: (at) / v = s / r

(ar) / v = s / t

(ar) / v = v, s / t becomes v because we have a distance over time which gives us velocity. However, this is only when we have s as a very small value. This is because as s gets smaller, the closer it is to the curvature of the circular path.

a = v2 / r, this is an equation of centripetal acceleration with respect to velocity because the radius remains constant.

We can derive the other equation by using the equation v = d / t. The distance of a circle is 2πr. We can substitute 2πr for d, which gets us: v = (2πr) / t. With this new information we can substitute (2πr) / t for v in the equation a = v2 / r.

a = ((2πr) / t)2 / r = (4π2r) / t2

a = (4π2r) / t2, this is the equation of centripetal acceleration with respect to time because the radius remains constant.

The acceleration is usually considered to be due to an inward acting force, which is known as the centripetal force. Centripetal force means “center seeking” force. It is the force that keeps an object in its uniform circular motion. We determine this force by using Newton's second law of motion, Fnet = ma, where Fnet is the net force acting on the object (this is the centripetal force, Fc, of an object in uniform circular motion), m is the mass of the object, and a is the acceleration of the object. Since the acceleration of the object in uniform circular motion is the centripetal acceleration, we can substitute v2 / r or (4π2r) / t2 for a. This gets us Fc = (mv2) / r or Fc = (4mπ2r) / t2

The centripetal force can be provided by many different things, such as tension (as in a string), and friction (as between a tire and the road).

An example of tension being the centripetal force is tying a mass onto a string and spinning it around in a horizontal circle above your head. The tension force is the centripetal force because it is the only force keeping the object in uniform circular motion.

Answer 4

A = arctan((v^2)/(rg))