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

Question

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

Quizplus · Accepted Answer

Explanation:The wheel's angular acceleration is 58 rad/s^2, and it accelerates from rest to 59 rad/s. We can use the equation:$$\omega^2 = \omega_0^2 + 2\alpha	heta$$where:$$\omega$$ is the final angular velocity (59 rad/s)$$\omega_0$$ is the initial angular velocity (0 rad/s)$$\alpha$$ is the angular acceleration (58 rad/s^2)$$	heta$$ is the angle through which the wheel turns (in radians)Plugging in the values, we get:$$59^2 = 0^2 + 2(58)	heta$$$$	heta = \frac{59^2}{2(58)} = 30 	ext{ rad}$$

A Wheel Accelerates from Rest to 59 Rad/s at a Uniform