Question

An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s ².
Through what angle has the record turned when its angular speed reaches 72.0 rad/s?

Answer 1

Answer:

$\theta = 947.7\ rad$

Explanation:

given,

initial rotating speed = 33.3 rad/s

angular acceleration = 2.15 rad/s²

final angular speed = 72 rad/s

using equation of rotating wheel

$\omega_f = \omega_i + \alpha t$

$72 = 33.3+ 2.15 t$

    2.15 t = 38.7

         t = 18 s

now, Again using equation of motion for the calculation of angle

$\theta = \omega_o t +\dfrac{1}{2}\alpha t^2$

$\theta = 33.3 \times 18 +\dfrac{1}{2}\times 2.15 \times 18^2$

$\theta = 947.7\ rad$

the angle record turned is equal to 947.7 radians.