Answer to Question #149906 in Mechanics | Relativity for Uuhh

Question

force of 2N in tangentially applied to a bicycle wheel for 4 seconds, then removed. If the moment of inertia of the wheel is 3 kg m² , The angular velocity of the wheel after 6 seconds. (radius of the wheel 30 cm) *

Answer 1

There formula of inertia: I = m × r²; (1)

The formula between force, mass and acceleration is: F = m$\times$ a; (2)

The formlua among acceleration, velocity, time and radius, angular velocity is: a = $\frac{v}{t} = \frac{w \times r}{t}$ ; (3)

We have: I=3 kg $\times$ m², F = 2 N, t = 6 s, R = 30 sm = 0.3 m.

Firstly, find mass by (1) formula:

m = $\frac{I}{r^2} = \frac{3}{0.3^2} = \frac{100}{3}(kg);$

Then, find a by (2) formula:

$a=\frac{F}{m} = \frac{2}{\frac{100}{3}}=\frac{6}{100} (\frac{m}{s^2})$ ;

Then, find angular velocity $w$ by (3) formula:

$w=\frac{a \times t}{r}=\frac{\frac{6}{100} \times 6}{0.3}=\frac{36}{30}=\frac{6}{5}=1.2 (\frac{1}{s})$ ;