# Torque with constant circular velocity

• Matejxx1
In summary: Nonetheless, there should still be a vertical force, according to the net force equation, and that vertical force should be sufficient to provide the centripetal force.[/b]In summary, the passenger with a height of 175cm is on a city bus with a center of mass at 110cm above the middle point of their 30cm long shoes. The bus is driving in a circle with a radius of 20m at a constant speed of 20 km/h. To prevent tipping over, the passenger needs to lean at an angle of 8.9° relative to the vertical axis, as calculated by the equation tanα = v^2/(r*g). Simply using the horizontal component of the weight is incorrect because the
Matejxx1

## Homework Statement

a passenger with height 175cmis driving on a city bus. The center of mass is at h=110cm above the middle point of the shoe which are 30 cm long. The passenger is standing in the direction of the ride.
h=175cm
h*=110cm
shoe size = 30 cm

b)
the bus is driving in a circle which has the radius of 20m with a constant speed of 20 km/h.For what angle relative to the vertical axis should the passenger lean so that he/she would not tip over.

Fc=m*v2/r
Fn=m*g*cosα
Fx=m*g*sinα

## The Attempt at a Solution

So here is what I tried to do
fc=m*(20/3,6)2/20..... I got Fc=1,543m
and here is something I don't understand. Since the centripetal force is acting toward the center of the circle, why is it incorrect to just use the Fx component of m*g
I tried doing it like this
Fc=1,543m Fx=m*g*sinα...since the body is not moving Torque=0
1,543m=m*g*sinα
sinα=(1.543*m)/(m*g) the masses cancel out
sin=1.543/9.8
sinα=0,157
α=9.05°

which is incorrect. The right answer is 8.9° and the end equation should look like this
tanα=v2/(r*g)
Can someone please explain or help me get to this equation tanα=v2/(r*g) [/b]

Last edited:
Matejxx1 said:
So here is what I tried to do
fc=m*(20/3,6)2/20..... I got Fc=1,543m
Are you given the mass of the passenger?
What are the units for Fc?

...and here is something I don't understand. Since the centripetal force is acting toward the center of the circle, why is it incorrect to just use the Fx component of m*g
... you mean the horizontal component of the weight?
Cartesian coordinates don't make a lot of sense here.

I tried doing it like this
Fc=1,543m Fx=m*g*sinα...since the body is not moving
... but the body is moving - in fact, for the term "centripetal force" to make sense, it must be accelerating: i.e. moving in a circle. So it must be acted on by an unbalanced force.

If I read you correctly, you tried to arrange to have zero horizontal force.

In the inertial frame, the net force on the body must point horizontally towards the center of the turn and sufficient to maintain circular motion. There should be zero net torque as well because the body has zero angular acceleration - it is rotating because it is constantly oriented along the axis of the turning bus.

## 1. What is torque with constant circular velocity?

Torque with constant circular velocity is the rotational force applied to an object moving in a circular path at a constant speed. It is a measure of how much a force applied at a certain distance from the center of rotation can cause the object to rotate.

## 2. How is torque with constant circular velocity calculated?

Torque with constant circular velocity is calculated by multiplying the force applied to the object by the distance from the center of rotation at which the force is applied. The unit of measurement for torque is Newton-meters (Nm) in the SI system.

## 3. What is the relationship between torque and angular velocity?

There is a direct relationship between torque and angular velocity. As torque increases, angular velocity also increases, and vice versa. This means that a larger torque will cause an object to rotate at a higher speed, while a smaller torque will result in a slower rotation.

## 4. How does torque with constant circular velocity affect rotational motion?

Torque with constant circular velocity is responsible for the rotational motion of an object. If there is no torque acting on an object, it will not rotate. Additionally, the direction of the torque determines the direction of the rotation.

## 5. What are some real-life examples of torque with constant circular velocity?

Examples of torque with constant circular velocity include the rotation of a bicycle wheel, the spinning of a top, and the movement of gears in a car's transmission. It is also a crucial concept in sports, such as figure skating and gymnastics, where athletes use torque to rotate their bodies in the air.

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