Question

An engine requires 5s to go from a speed of 600 r.P.M. To 1200 r.P.M. With constant acceleration how many revolution does it make in this period

Answer 1

Answer:

75 revolution.

Explanation:

Refer to the material.

Answer 2

75 revolutions are made.

Given:

• Initial angular velocity = 600 rpm
• Final angular velocity = 1200 rpm
• Time = 5 sec

To find:

Number of revolutions made ?

Calculation:

First of all, let us calculate the angular acceleration.

• 600 rpm = 600 × 2π/60 = 20π rad/s
• 1200 rpm = 1200 × 2π/60 = 40π rad/s.

Now, we can say:

$\omega = \omega_{o} + \alpha t$

$\implies \: 40\pi = 20\pi + \alpha (5)$

$\implies \: 5 \alpha = 20\pi$

$\implies \: \alpha = 4\pi \: rad \: {s}^{ - 2}$

Now, we can say:

${ \omega}^{2} = { \omega_{o}}^{2} + 2 \alpha \theta$

$\implies \: 1600 {\pi}^{2} = 400 {\pi}^{2} + 2(4\pi) \theta$

$\implies \: 8\pi\theta = 1200 {\pi}^{2}$

$\implies \: \theta = 150 \pi \: rad$

$\implies \: \theta = \dfrac{ 150 \pi }{2\pi}\: rev$

$\implies \: \theta =75\: rev$

So, 75 revolutions were made.