Circular motion: bicycle moving in a circle. Find speed given r and degree

• s1gma
In summary, the problem involves a bicycle racing in a circle of radius 19 m, with a force exerted by the road at an angle of 23 degrees with the vertical. Using the equations for uniform circular motion, the tangential velocity (v) can be solved for. After breaking down the angle into component vectors and setting up equations for the x and y components, the solution was found to be 8.89 m/s.
s1gma

Homework Statement

A bicycle is racing around on a horizontal surface in a circle of radius 19 m. The force exerted by the road on the bicycle makes an angle of 23 degrees with the vertical. What is its speed?

Homework Equations

I believe this is a uniform circular motion problem, so I've been trying these equations:

$$\Sigma$$ F = ma

a = $$\frac{v^{2}}{r}$$

Where v is the tangential velocity (what I need to find) and a is the acceleration pointing inward causing it to turn, r is the radius.

The Attempt at a Solution

I thought this problem was a mistake at first because I'm given an angle and a radius, and I'm somehow supposed to derive a speed. I broke down the angle into component vectors where x = 0.39 and y = 0.92. I know that the x component points inward to the center of the circle and should be the radial component for a circular motion problem. I could use that as a then just plug in r and solve for v.

However, I don't know the real magnitude of the force from the earth, so I don't know how to find a. This is the only way to solve it that I can think of. Can someone guide me here?

Got it! After looking it over for a while I started from the beginning, this time setting up the y equation so we have:

Fnet x = n*sin(theta) = (mv^2) / (r)
Fnet y = n*cos(theta) - mg = 0

You can solve the y equation for n and then plug it into the n of the x equation so that the mass cancels out and you eventually end up with just the radius, g, and tangent of the angle theta which are all known. Solution was 8.89 m/s.

Thanks anyway.

1. What is circular motion?

Circular motion is a type of motion where an object moves along a circular path. It occurs when the object's velocity is constantly changing, but its speed remains constant.

2. How does a bicycle move in a circle?

A bicycle moves in a circle when the rider applies a centripetal force towards the center of the circle, causing the bicycle to turn. The force is provided by the friction between the tires and the ground, as well as the handlebars and the rider's body weight.

3. What is the relationship between speed and radius in circular motion?

The speed of an object in circular motion is directly proportional to the radius of the circle. This means that as the radius increases, the speed also increases, and vice versa. This relationship is described by the equation v = rω, where v is the speed, r is the radius, and ω is the angular velocity.

4. How can you find the speed of a bicycle moving in a circle given the radius and degree of rotation?

To find the speed of a bicycle moving in a circle, you can use the formula v = 2πr(n/T), where v is the speed, r is the radius, n is the number of rotations, and T is the time it takes for the bicycle to complete those rotations. If the degree of rotation is given, you can convert it to radians by multiplying it by π/180 before plugging it into the formula.

5. Can the speed of a bicycle moving in a circle ever be constant?

Yes, the speed of a bicycle moving in a circle can be constant if the radius and angular velocity remain constant. This means that the centripetal force and all other forces acting on the bicycle are balanced, resulting in a constant speed. However, the direction of the bicycle's motion will constantly change as it moves along the circular path.

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