A wheel has angular acceleration of 3.0 rad/sec² and an initial angular speed of 2.00 rad/sec². In a time of 2 sec, it has rotated through an angle (in radian) of

A wheel rotates from rest at an initial angular speed of 2.00 rad/s with a constant angular acceleration of 3.0 rad/s 2. Over a time interval of 2 s, the total angle through which the wheel rotates can be determined by combining contributions from its initial angular speed and acceleration.

The angular displacement depends on two factors: how much the wheel rotates due to its initial speed and how much it accelerates during the given time. The rotation caused by the initial speed is just the product of the angular speed and time, which accounts for a certain number of radians. The additional rotation comes from the angular acceleration, which increases the wheel’s speed over time, causing more rotation.

The total rotation over those 2 s is the sum of these two contributions. In this example, the angle that is rotated solely due to initial velocity is 4 rad; the acceleration adds in an additional 6 rad to the rotation over the same 2 s period. So a total angular displacement of 10 rad would be completed in the 2 s time duration.

This calculation illustrates the combination of the initial angular motion with constant acceleration as leading to an increase in the total angle rotated over time.

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