- #1

- 62

- 6

## Homework Statement

We have a bicycle and lift the front wheel. And with the hand we apply a force of 10 N down and we turn the wheel. The wheel is 26 inches in diameter and weighs 1.5 kg. Find the angular acceleration, the torque of the net force and the angular velocity after a lap.

## Homework Equations

r=d/2; F=ma_t=mrα; Γ=mr

^{2}α...

## The Attempt at a Solution

Data:

vector(F)=10 N

d=26''

m=1,5 kg

The first step is to pass the data into units of the international system (S.I), and then look for the radius of the wheel. The only data that is not in units of S.I is the diameter, therefore

26 · (0,0254 m)(1) = 0,66 m

r=d/2 → r=(0,66)/2=0,33 m

Once we are going to calculate the angular acceleration. Based on the formula of Newton's second law and since the force we exercise already acts in the tangential direction we isolate and replace:

F=ma

_{t}=mrα→α=F/mr→α=10/(1,5·0,33)=20,2 rad/s

^{2}

To find the pair of the net force is done by means of the following formula:

Γ

_{net}=mr

^{2}α→Γ

_{net}=1,5·0,33

^{2}·20,2=3,3 N·m

And finally we calculate the angular velocity after a turn. One turn is 360 degrees which radiant is equivalent to 2π rad

ω

^{2}=ω

_{0}

^{2}+2αφ→ω=sqrt(2αφ)→ω=sqrt(2·20,2·2π)=15,93 rad/s

Is this exercise well resolved? What could be added so that it was more physically solved? And any idea to include in the exercise or modify it?