# Angled cyclist turn

The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?

**Result****Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):**

**Showing 1 comment:**

**Matematik**

A cyclist has to bend slightly towards the center of the circular track in order to make a safe turn without slipping.

Let m be the mass of the cyclist along with the bicycle and v, the velocity. When the cyclist negotiates the curve, he bends inwards from the vertical, by an angle θ. Let R be the reaction of the ground on the cyclist. The reaction R may be resolved into two components:

(i) the component R sin θ, acting towards the center of the curve providing necessary centripetal force for circular motion and

(ii) the component R cos θ, balancing the weight of the cyclist along with the bicycle.

Thus for less bending of the cyclist (i.e for θ to be small), the velocity v should be smaller and radius r should be larger. let h be the elevation of the outer edge of the road above the inner

edge and l be the width of the road then,

Let m be the mass of the cyclist along with the bicycle and v, the velocity. When the cyclist negotiates the curve, he bends inwards from the vertical, by an angle θ. Let R be the reaction of the ground on the cyclist. The reaction R may be resolved into two components:

(i) the component R sin θ, acting towards the center of the curve providing necessary centripetal force for circular motion and

(ii) the component R cos θ, balancing the weight of the cyclist along with the bicycle.

Thus for less bending of the cyclist (i.e for θ to be small), the velocity v should be smaller and radius r should be larger. let h be the elevation of the outer edge of the road above the inner

edge and l be the width of the road then,

Tips to related online calculators

Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

Do you want to convert mass units?

Do you want to convert velocity (speed) units?

See also our right triangle calculator.

See also our trigonometric triangle calculator.

Try conversion angle units angle degrees, minutes, seconds, radians, grads.

Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

Do you want to convert mass units?

Do you want to convert velocity (speed) units?

See also our right triangle calculator.

See also our trigonometric triangle calculator.

Try conversion angle units angle degrees, minutes, seconds, radians, grads.

#### Following knowledge from mathematics are needed to solve this word math problem:

## Next similar math problems:

- The trapezium

The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium. - Trapezoid MO-5-Z8

ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm^{2}. Determine the area of the trapezoid - Eq triangle minus arcs

In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts - Quadrilateral 2

Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles. - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Circular railway

The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C? - Ratio of sides

Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7. - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Hexagonal pyramid

Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. - Company logo

The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo? - Area of a rectangle

Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem. - Annular area

The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area. - Circular ring

Square with area 16 centimeters square are inscribed circle k1 and described circle k2. Calculate the area of circular ring, which circles k1, k2 form. - Rectangle

In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - 30-gon

At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area. - Squares above sides

Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm^{2}. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc - The sides 2

The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.