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A wheel rotates with constant aceeleration of $2.0\; rad/s^2$ , if the wheel starts from rest the number of revolutions it makes in the first ten seconds will be approximately
Option: 1
16

Option: 2
24

Option: 3
32

Option: 4
8

Answers (1)

best_answer

As we have learned

Time period -Time taken to complete one rotation

S.I unit seconds (s)

$w= \frac{2\pi }{T } \: \: \: or \; \; \frac{2\pi N}{T}$

N= Number of rotation

$w= 2\pi \nu$

$\nu = \frac{N}{t}$

For circular/angular motion, the formula for angular displacement $\theta$ and angular acceleration $\alpha$ is

$\theta =\omega +\frac{1}{2}\alpha t^2$

where $\omega$ =intial angular velocity

$\theta =0+\frac{1}{2}\alpha t^2=\frac{1}{2}\times(2)\times(10)^2$

or

$\theta=100 \; radian$

$2\pi$ radian is covered in 1 revolution

$\therefore$ 1 radian is coverd in $\frac{1}{2\pi}$ revolution

100 radians are covered in $\frac{100}{2\pi}$ revolution

$\therefore$ Number of revolution $=\frac{50}{3.14}\approx 16$

Posted by

Ritika Kankaria

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