Question

a stationary wheel starts rotating about its own axis at an angular acceleration 5.5 rad per sec^2.to acquire an angular velocity 420 revolutions per minute,the number of rotations made by the wheel is

Answer 1

Explanation:

Wf=420rpm

=420×2pie÷60 rad/sec.

alpha=5.5rad/sec^2

wf^2=2alpha×theta

196pie^2=11theta

theta is also = 2pieN

so,196pie^2=11×2×pie×N

therefore by solving we get N=28

Answer 2

$n=1679.324\ revolutions$ is the approximate total revolutions made.

Explanation:

Given:

initial angular speed, $N_0=0\ rpm$

final angular speed, $N=420\ rpm$

angular acceleration, $\alpha=5.5\ rad.s^{-2} =\frac{5.5\times 60}{2\pi} =\frac{165 }{\pi}\ rev.min^{-2}$

Now, using the equation of motion:

$N^2=N_0^2+2\alpha.n$

where, n = no. of revolutions

$420^2=0^2+2\times \frac{165}{\pi} \times n$

$n=1679.324\ revolutions$

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TOPIC:equation of motion applied to angular motion

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