Sage-Tips

What is the radius of curvature of the resulting trajectory at its apex in m )?

Radius of curvature is infinity till it reaches highest point and at the highest point it is zero, then downwards its again infinity.

What is radius of curvature in circular motion?

In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof.

What is the trajectory of a projectile and what is its shape?

Objects experiencing projectile motion have a constant velocity in the horizontal direction, and a constantly changing velocity in the vertical direction. The trajectory resulting from this combination always has the shape of a parabola.

What is the radius of curvature of a particle?

For any point on a curve, the radius of curvature is 1/κ. In other words, the radius of curvature is the radius of a circle with the same instantaneous curvature as the curve. so that by the second of the results in (*) T′(t) = N(t)‖T′(t)‖ = ‖r′(t)‖κ(t)N(t).

What is radius of curvature at highest point?

Radius of curvature at maximum height At maximum height, angle that the velocity vector makes with the horizontal, . So, radius of curvature at maximum height = u 2 cos 2 ⁡ .

How do you find the radius of curvature of a trajectory?

The curvature(K) of a path is measured using the radius of the curvature of the path at the given point. If y = f(x) is a curve at a particular point, then the formula for curvature is given as K = 1/R.

What is the difference between radius and radius of curvature?

Difference Between Radius and Radius of Curvature Radius refers to the distance between the center of a circle or any other point on the circumference of the circle and surface of the sphere. While on the other hand, the radius of curvature is the radius of the circle that touches the curve at a given point.

How do you find the trajectory of a projectile?

Trajectory formula

1. x = Vx * t => t = x / Vx.
2. y = h + Vy * t – g * t² / 2 = h + x * Vy / Vx – g * (x / Vx)² / 2.
3. y = h + x * (V₀ * sin(α)) / (V₀ * cos(α)) – g * (x / V₀ * cos(α))² / 2.

How do you find the radius of curvature of a Class 10?

10 cm. Hint:The radius of curvature of convex or concave mirror is equal to two times of the focal length of convex or concave mirror. The radius of curvature is the radius of sphere formed by the convex or concave mirror. It is also equal to the distance between the pole and centre of curvature.

What is the radius of trajectory of projectile?

Radius of trajectory of a projectile at a point along it’s trajectory is the radius of circular arc which best approximates the curve at that point and tells us how the trajectory of the projectile is curving at that point.

How do you find the radius of curvature of a curved path?

Radius of curvature of any curved path, at some point on it, is given by: You can now use the expression of your trajectory. where and are the x and y components of velocity at some point and and are the x and y components of acceleration at the same point You can use either. Let be the centripetal acceleration.

What does the curvature of an object at the top mean?

For example, smaller radius of curvature at the top (i.e. at the point of maximum height) means it curves more at the top, than say, at the launch or landing point where it curves less.

Why is the trajectory of a projectile a parabola?

When a particle moves along a curved path, it is continuously acted upon by centripetal force. Then only motion along a curve will be possible. Now, trajectory of a projectile is parabola, a curved path. The centripetal force at each point is provided by appropriate component of mg in the direction of radius of curvature at the point concerned.