Linear acceleration of bicycle

[bocobuff]

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
a_rad=ω²*r
a_tan=r*α
a_total=√a_rad²+a_tan²

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 a_tan=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 a_rad?? Do you use both and add them together to use for a_total or the change in a_rad? Also, do I have to multiply the final total accel by 2 since there are two wheels?

 

[asleight]

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
a_rad=ω²*r
a_tan=r*α
a_total=√a_rad²+a_tan²

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 a_tan=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 a_rad?? Do you use both and add them together to use for a_total or the change in a_rad? 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. ;)

 

[bocobuff]

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.

 

[asleight]

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.