Question

3. A wheel rotates with a constant angular acceleration of 3.50 rad/s^2 . (a) If the angular speed of the wheel is 2.00 rad at t = 0, through what angular displacement does the wheel rotate in 2.00 sec? (b) Through how many revolutions has the wheel turned during this time interval? (c) What is the angular speed of the wheel at t = 2.00 sec?



4. A wheel is rotating at 4000 rpm. The wheel is decelerated at a rate of 20 rad/s^2 . Through how many revolutions will it rotate before it stops?

Answer 1

3.

(a)

$\phi=\omega_0t+\frac{\epsilon t^2}{2}=2\cdot2+\frac{3.5\cdot2^2}{2}=11 rad$

(b)

$n=\frac{\phi}{2\pi}=\frac{11}{2\pi}=1.75$

(c)

$\omega=\omega_0+\epsilon t=2+3.5\cdot2=9rad/s$

4.

$4000rpm\approx419rad/s$

$\omega=\omega_0-\epsilon t\to0=\omega_0-\epsilon t\to t=\omega_0/\epsilon=419/20\approx21s$

$\phi=\omega_0t-\frac{\epsilon t^2}{2}=419\cdot21-\frac{20\cdot21^2}{2}=4389 rad$

$n=\frac{\phi}{2\pi}=\frac{4389}{2\pi}=698.5$