Question

A wheel has angular acceleration of $3.0 \,rad/sec^{-2}$ and an initial angular speed of $2.00\, rad\,s^{-1}$. In a time of $2\, s$ it has rotated through an angle (in radian) of

• A. 10
• B. 12
• C. 4
• D. 6

Answer 1

The Correct Option is A

To solve the problem of determining the angle through which the wheel has rotated, we will use the equation of rotational motion:

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

where:

• \theta is the angle in radians the wheel has rotated through.
• \omega_0 = 2.00 \, \text{rad/s} is the initial angular speed.
• \alpha = 3.0 \, \text{rad/s}^2 is the angular acceleration.
• t = 2 \, \text{s} is the time duration.

Plug the values into the formula:

\theta = 2.00 \times 2 + \frac{1}{2} \times 3.0 \times (2)^2

Simplify the terms step-by-step:

1. Calculate the first term: 2.00 \times 2 = 4.00 \, \text{rad}
2. Calculate the second term: \frac{1}{2} \times 3.0 \times 4 = 6.00 \, \text{rad}

Adding these results gives:

\theta = 4.00 + 6.00 = 10.00 \, \text{rad}

Therefore, the wheel has rotated through an angle of 10 radians in 2 seconds.

The correct answer is 10.