A bicycle has wheels with a diameter of 0.570 m. It accelerates uniformly and the rate of rotation of its wheels increases from 181 rpm to 260 rpm in a time of 19.9 s. Find the linear acceleration of the bicycle.
i tried converting everything to linear to use a linear equation but i cant get the right answer
wi=181rpm=2pi(181/60)=18.95rad/s wf=260rpm=2pi(260/60)=27.23rad/s angular acceleration=a/r=wf-wi/t a/0.285=27.23-18.95/19.9 3.51a=0.416 a=0.12m/s^2
To find the linear acceleration of the bicycle, we need to convert the rotations per minute (rpm) to radians per second (rad/s) and then use the formula for linear acceleration.
1. Convert the initial and final rotations per minute (rpm) to radians per second (rad/s):
- Initial angular velocity, ω₁ = (181 rpm) * (2π rad/1 min) * (1 min / 60 s) = 19.023 rad/s
- Final angular velocity, ω₂ = (260 rpm) * (2π rad/1 min) * (1 min / 60 s) = 27.275 rad/s
2. Calculate the change in angular velocity (Δω) = ω₂ - ω₁:
Δω = 27.275 rad/s - 19.023 rad/s = 8.252 rad/s
3. Determine the time taken (Δt) = 19.9 s.
4. Use the formula for linear acceleration:
Linear acceleration (a) = Δω / Δt
Substituting the values:
a = 8.252 rad/s / 19.9 s ≈ 0.414 m/s²
Therefore, the linear acceleration of the bicycle is approximately 0.414 m/s².