Linear acceleration of bicycle

In summary, a bicycle with wheels of radius 0.295 m accelerates uniformly from 209 rpm to 265 rpm in 20.7 s. Using the equations α=Δω/Δt and atan=r*α, the linear acceleration is found to be 0.0835 m*radians/s2. This value does not need to be multiplied by 2 since it is the acceleration of one wheel, which is equivalent to the acceleration of the whole bicycle.
  • #1
bocobuff
42
0

Homework Statement


A bicycle has wheels with a radius of 0.295 m. It accelerates uniformly and the rate of rotation of its wheels increases form 209 rpm to 265 rpm in a time of 20.7 s. What is the linear acceleration of the bicycle?
ω=angular vel. α=angular accel.

Homework Equations


rev/min*2π*1/60s= rad/s
α=Δω/Δt
arad2*r
atan=r*α
atotal=√arad2+atan2

The Attempt at a Solution


First changed rpm to radian/s so ω1=21.89 radian/s and ω2=27.75 radian/s
For α=Δω/Δt=(27.75-21.89)/20.7s=0.283 radians/s2
Then got atan=0.295 m*0.283 radians/s2=0.0835 m*radians/s2
But I don't know if I should use ω1 or ω2 for the arad?? Do you use both and add them together to use for atotal or the change in arad? Also, do I have to multiply the final total accel by 2 since there are two wheels?
 
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  • #2
bocobuff said:

Homework Statement


A bicycle has wheels with a radius of 0.295 m. It accelerates uniformly and the rate of rotation of its wheels increases form 209 rpm to 265 rpm in a time of 20.7 s. What is the linear acceleration of the bicycle?
ω=angular vel. α=angular accel.

Homework Equations


rev/min*2π*1/60s= rad/s
α=Δω/Δt
arad2*r
atan=r*α
atotal=√arad2+atan2

The Attempt at a Solution


First changed rpm to radian/s so ω1=21.89 radian/s and ω2=27.75 radian/s
For α=Δω/Δt=(27.75-21.89)/20.7s=0.283 radians/s2
Then got atan=0.295 m*0.283 radians/s2=0.0835 m*radians/s2
But I don't know if I should use ω1 or ω2 for the arad?? Do you use both and add them together to use for atotal or the change in arad? Also, do I have to multiply the final total accel by 2 since there are two wheels?

Why do you want to find the radial acceleration of the bike? That won't give you its linear acceleration at all. ;)
 
  • #3
Ahh... I gotcha. Thanks a lot. But do I need to multiply it by 2 since there are two wheels and it's asking for the whole bicycle? I know this is stupid but I only have one submission on my HW left so I need to get this one.
 
  • #4
bocobuff said:
Ahh... I gotcha. Thanks a lot. But do I need to multiply it by 2 since there are two wheels and it's asking for the whole bicycle? I know this is stupid but I only have one submission on my HW left so I need to get this one.

No. You're fine by solving the acceleration of one wheel, as far as I'm concerned.
 

1. What is linear acceleration of a bicycle?

Linear acceleration of a bicycle refers to the rate of change of its velocity in a straight line. It measures how fast the bike is gaining speed or slowing down in a straight line.

2. How is linear acceleration different from angular acceleration?

Linear acceleration refers to the change in velocity in a straight line, while angular acceleration refers to the change in rotational velocity. In other words, linear acceleration is the acceleration of an object moving along a linear path, while angular acceleration is the acceleration of an object rotating around a fixed axis.

3. What factors affect the linear acceleration of a bicycle?

The linear acceleration of a bicycle is affected by several factors, including the force applied to the pedals, the weight of the bike and rider, the slope of the terrain, and air resistance. The type and condition of the tires and the surface of the road can also impact linear acceleration.

4. How can the linear acceleration of a bicycle be calculated?

The linear acceleration of a bicycle can be calculated by dividing the change in velocity by the change in time. This can be represented by the equation a = (v2 - v1) / t, where a is acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the change in time.

5. How can linear acceleration be used to improve bike performance?

By understanding the factors that affect linear acceleration, cyclists can make adjustments to their bike and riding technique to improve performance. For example, reducing air resistance by maintaining an aerodynamic position or using smoother tires can increase linear acceleration. Additionally, applying more force to the pedals or reducing the weight of the bike can also improve linear acceleration.

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