Question

A rotating wheel requires 5.00 s to rotate 26.0 revolutions. Its angular velocity at the end of the 5.00 s interval is 95.0 rad/s. What is the constant angular acceleration of the wheel?
_________ rad/s²

Answer 1

Since angular acceleration is constant, therefore we use equations of motion for angular motion,

1) w_{​​​​​f} = w_{​​​​​​I} + $\alpha$ t

wf - final angular velocity

wi - initial angular velocity

$\alpha$ - angular acceleration

t - time taken

2) $\theta$ = w_{​​​​​​i}​​​t + 1/2 $\alpha$ t²

^{$\theta$ - angular displacement}

t= 5s

w​​​​​​​F = 95 rad/s

$\theta$= no. Of revolution x 2π = 26x2π = 52π

Putting in equations,

1) 95 = wi + $\alpha$ (5)

=> Wi = 95-5a

2) 52π = 5Wi + (1/2)(25)$\alpha$

Using 1

52π = 5(95-5a) + 12.5a

=> 12.5a = 475-52(3.14) = 311.72

=> $\alpha$ = 311.72/12.5 = 24.93 rad/s^{​​​​​​2}