A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle θ_1 and in the next 2 s it rotates through an angle θ_2 . The ratio (θ_2)/(θ_1) is

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Quantrex Academy · Accepted Answer

Correct answer: B. 3

Using the equation of rotational kinematics

\theta = \omega_0 t + \dfrac{1}{2} \alpha t^2

.

Since the wheel is initially at rest,

\omega_0 = 0

.

Angle rotated in the first

2\text{ s}

:

\theta_1 = \dfrac{1}{2} \alpha (2)^2 = 2\alpha

Angle rotated in the first

4\text{ s}

:

\theta_{total} = \dfrac{1}{2} \alpha (4)^2 = 8\alpha

Angle rotated in the next

2\text{ s}

:

\theta_2 = \theta_{total} - \theta_1 = 8\alpha - 2\alpha = 6\alpha

The ratio is:

\dfrac{\theta_2}{\theta_1} = \dfrac{6\alpha}{2\alpha} = 3

Answer:

3

A wheel initially at rest is subjected to a uniform angular...

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