Question

Car's wheel accelerates at 22.4 radians per second squared. If the wheel begins with an angular speed of 10.8 radians per second. What is the wheel's angular speed after 3 full turns?

Answer 1

Answer:

Final angular speed of the wheel is given as

$\omega = 31 rad/s$

Explanation:

Angle of revolution of the car wheel is

N = 3 turns

in one turn it will revolve by $2\pi$ angle

so we have

$\theta = 3(2\pi)$

$\theta = 6\pi$

now we can use kinematic to find the final speed

$\omega^2 - \omega_0^2 = 2\alpha \theta$

so we have

$\omega^2 - 10.8^2 = 2(22.4)(6\pi)$

$\omega^2 = 10.8^2 + 844.5$

$\omega = 31 rad/s$