Question

At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of -0. 40 rad/s2 has an angular velocity of 1. 5 rad/s and an angular position of 2. 3 rad. What is the angular position of the wheel at t = 2. 0 s?.

Answer 1

The angular position of the wheel at t = 2. 0 s is 4.5 rad.

Angular Position:

When an object is undergoing a rotational motion, then the orientation of the object with respect to a specific reference position is known as angular position.

Given data:

The angular acceleration of the object at initial is, α = - 0.40 rad/s².

The angular velocity of the object is, ω = 1.5 rad/s.

The angular position of the object at initial is, $\theta = 2.3 \;\rm rad$.

The time interval is, t = 2.0 s.

The expression for the angular position of the wheel at t = 2.0 s is,

$\theta' = \theta+ \omega t + \dfrac{1}{2} \alpha t^{2}$

Solving as,

$\theta' = 2.3+ (1.5 \times 2) + \dfrac{1}{2} \times (-0.40) \times 2^{2}\\\\ \theta' = 4.5 \;\rm rad$

Thus, we can conclude that the angular position of the wheel at t = 2. 0 s is 4.5 rad.

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