How to calculate torque required to accelerate

  • Context: Undergrad 
  • Thread starter Thread starter gearhead
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Discussion Overview

The discussion revolves around calculating the torque required to accelerate a bicycle with a rider, focusing on two specific scenarios: overcoming static friction to initiate movement and achieving a specified acceleration rate. The scope includes theoretical calculations and assumptions regarding forces and friction.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks to calculate the torque needed to break static friction and accelerate a bicycle weighing 100 kilograms.
  • Another participant states that torque is related to force and wheel radius, providing the formula τ = RF.
  • A participant calculates the force of static friction as 490N, leading to a torque requirement of 176.86N*m to overcome friction.
  • One participant suggests that the static friction to be overcome is primarily between the axle and the bearings, rather than the ground.
  • Another participant notes the importance of the axle radius in torque calculations.
  • A participant questions whether any amount of torque generated would lead to forward acceleration.
  • One participant calculates the torque required for an acceleration of 1m/s² as 36.1N*m, using the force derived from F=ma.

Areas of Agreement / Disagreement

Participants express differing interpretations of the forces involved in the torque calculations, particularly regarding static friction and the role of the axle. There is no consensus on the exact torque values or the assumptions made in the calculations.

Contextual Notes

Participants have not fully resolved the assumptions regarding the static coefficient of friction, the role of rolling resistance, and the specific conditions under which the calculations apply.

gearhead
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I have a bicycle that has a mass of 100kilograms with the rider on it. The wheels have a diameter of 26" or 0.722meters. How do i calculate how much torque is required to: 1.) break the static coefficient of friction and cause the wheel to start turning, and 2.) determine how much torque is required to accelerate at a rate of 1m/s^2?
 
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Assuming no slipping, the torque, [itex]\tau[/itex], delivered to the wheels of radius, R, is related to the force, F, that pushes the vehicle by

[tex]\tau=RF[/itex][/tex]
 
so then i must calculate the force of static friction on the bike first to determine the amount of torque required to overcome this. F=ma, f=100(9.8) = 980N*0.5(the static coefficient of friction)=Force of friction=490N. So then required torque is then, t=0.361m*490=176.86N*m of torque to counteract friction and cause the wheel to start turning.
 
gearhead said:
I have a bicycle … How do i calculate how much torque is required to: 1.) break the static coefficient of friction and cause the wheel to start turning

Hi gearhead! :smile:

The wheel does not move relative to the ground, so the static friction to be overcome is only between the axle and the bearings.

For deformable wheels (eg rubber), there is also rolling resistance (loss of energy through deformation … it's what slows the Moon down!): see http://en.wikipedia.org/wiki/Rolling_resistance :wink:
 
tiny-tim said:
... the static friction to be overcome is only between the axle and the bearings.
Ah, yes, that is a better interpretation of the question than what I was thinking of. Then gearhead will also need the radius of the axle.
 
oh allright, thanks guys, so then theoretically any amount of torque you generate will accelerate you forward right?
 
so then, i'll try to calculate the amount of torque required to accelerate the bike at 1m/s^2.
using
F=ma, F=(100kg)*(1m/s^2)=100Newtons.
T=R*F. T=(0.361m)*(100N)=36.1N*m of torque, right?
 

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