how do i find the lever arm?

[dl09]

let's say we have an electric car. the electric motor turns the wheels. there is a torque. torque is force times lever arm. is the distance from the center of the wheel to the edge of the wheel, the lever arm? if not, then where is the lever arm?

[swansont]

T = r x F

r is the distance from the axis of rotation to the point where the force is applied. In this case it would be the radius of the axle, if the force was being applied there. The torque from friction on the wheel would use the distance to the edge of the wheel, since that force is applied at the edge.

[dl09]

so the radius of the axle is the lever arm? just trying to make sure i understand the post.

[studiot]

43 minutes ago, dl09 said:

so the radius of the axle is the lever arm? just trying to make sure i understand the post.

 

You had the right of it.

"Torque is force times lever arm."

Ignoring losses the engine output shaft has cogs solidly affixed which mesh with cogs afffixed to the wheel drive shaft.
Both of these are much smaller radius than the wheel itself.

The torque transferred from the engine to the wheel is constant throughout (though different for different speeds etc) since we are ignoring .

If we call this T then T = R_shaft x F_cog

F_cog = the contact or pressure force between the engine cog and the wheel shaft cog.

At the wheel the torque is transferred to the road by the friction between the tyre and the road.

T = R_wheel x F_{tyre friction}

Since both torques are the same

R_shaft x F_cog = R_wheel x F_{tyre friction}

 

Does this help?

[swansont]

1 hour ago, dl09 said:

so the radius of the axle is the lever arm? just trying to make sure i understand the post.

Yes, if that's where the force is being applied.

As studiot points out, if there is no angular acceleration the two torques present (one on the shaft, on on the edge of the wheel) must be equal in magnitude.

[dl09]

i am planning to build a robotic toy car. if i punch a hole in a bottle cap and insert the shaft of the electric motor in the hole, then the lever arm is the radius of the electric motor shaft?