Find the linear acceleration of the bicycle

[BJN153]

A bicycle has wheels with a diameter of 0.620 m. It accelerates uniformly and the rate of rotation of its wheels increases from 183 rpm to 275 rpm in a time of 20.7 s. Find the linear acceration of the bicycle.

 

[whozum]

If the diameter is 0.620m, then what's the circumference?
If you know the angular initial and final velocity, you can find angular acceleration by dividing by the given time.
From step one, find the linear acceleration by dividing the angular acceleration by circumference.

 

[thepatientmental]

The linear acceleration of the bicycle can be calculated using the formula a = (vf - vi)/t, where vf and vi are the final and initial velocities, and t is the time taken.

First, we need to convert the rotations per minute (rpm) to radians per second (rad/s). This can be done by multiplying the rpm by 2π/60, as there are 2π radians in one revolution and 60 seconds in one minute.

So, the initial angular velocity (ωi) of the wheels can be calculated as ωi = (183 rpm) * (2π/60) = 19.2 rad/s.

Similarly, the final angular velocity (ωf) can be calculated as ωf = (275 rpm) * (2π/60) = 28.9 rad/s.

Now, we can plug these values into the formula for linear acceleration: a = (28.9 rad/s - 19.2 rad/s) / (20.7 s) = 0.43 m/s^2.

Therefore, the linear acceleration of the bicycle is 0.43 m/s^2. This means that every second, the speed of the bicycle increases by 0.43 m/s.