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.

Answer 2

The angle at which the wheel turns while accelerating is 30 radians and this can be determined by using the kinematics equation.

Given :

A wheel accelerates from rest to 59 rad/$\rm s^2$ at a uniform rate of 58 rad/$\rm s^2$.

The equation of kinematics is used in order to determine the angle at which the wheel turn while accelerating.

$\omega^2 = \omega^2_0+2\alpha \theta$

where $\omega$ is the final angular velocity, $\omega_0$ is the initial angular velocity, $\alpha$ is the angular acceleration, and $\theta$ is the angular displacement.

Now, substitute the values of the known terms in the above formula.

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

Simplify the above expression.

$\rm \theta = 30\; rad$

Therefore, the correct option is C).

For more information, refer to the link given below:

https://brainly.com/question/408236