# Torque with constant circular velocity

**1. The problem statement, all variables and given/known data**

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.

**2. Relevant equations**

**F _{c}=m*v^{2}/r**

F_{n}=m*g*cosα

F_{x}=m*g*sinα

**3. The attempt at a solution**

So here is what I tried to do

**f _{c}=m*(20/3,6)^{2}/20……………… I got F_{c}=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 F

_{x}component of m*g

I tried doing it like this

**F**

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°

_{c}=1,543m F_{x}=m*g*sinα……since the body is not moving Torque=01,543m=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=v

^{2}/(r*g)

Can someone please explain or help me get to this equation tanα=v

^{2}/(r*g) [/b]

**Thank you for reading**

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