At t = 0, a wheel rotating about a fixed axis at a constant angular deceleration of 0.5 rad/s 2 has an angular velocity of 4.2 rad/s and an angular position of 6.8 rad. What is the angular position of the wheel after 2 s? Answer in units of rad.

The angular position of the wheel after 2 s is 14.8 rad.

Explanation:

From the equation of motion, we have

Δs = u·t + 1/2·α·t²

Where Δs = Change in position of a point on the wheel

u = Initial angular velocity at time t = 0, = 4.5 rad/s

t = Time duration of the motion = 2 s

α = Angular acceleration = -0.5 rad/s²

Therefore

Δs = u·t + 1/2·α·t²  = 4.5×2 + 1/2×(-0.5)×2² = 8 radians

Where we have the initial position to be 6.8 rad, the new position therefore,  will be

6.8 rad + 8 rad = 14.8 rad.

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