Question

A wheel accelerates from rest to 59 rad/s^2 at a uniform rate of 58 rad/s^2. Through what angle (in radians) did the wheel turn while accelerating?
A) 24 rad
B) 38 rad
C) 30 rad
D) 60 rad

Answer 1

To solve this problem we will apply the physical equations of the angular kinematic movement, for which it defines the square of the final angular velocity as the sum between the square of the initial angular velocity and the product between 2 times the angular acceleration and angular displacement. We will clear said angular displacement to find the correct response

Using,

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

Here,

$\omega$ = Final angular velocity

$\omega_0$ = Initial angular velocity

$\alpha =$ Angular acceleration

$\theta =$ Angular displacement

Replacing,

$59^2 = 0+2*58\theta$

$\theta = 30rad$

Therefore the correct answer is C.