Question

14. FIGURE Q4.14 shows four rotating wheels. For each, determine the signs $(+$or $-)$of $\omega$and $\alpha$.

Short answer

For wheel$\left(\text{a}\right):\omega =-,\alpha =+$

For wheel (b):$\omega =+,\alpha =-$

For wheel (c):$\omega =-,\alpha =-$

For wheel (d):$\omega =+,\alpha =+$

Step-by-step solution

Part (a)

As the wheel (a) is rotating in counter-clock wise direction therefore the sign of angular velocity as $\omega =-\text{\hspace{0.05em}ve}$, and since the wheel is speeding up, therefore the angular acceleration$\alpha =(+)\text{\hspace{0.05em}ve}$

Part (b)

As the wheel (b) is rotating in clock wise direction therefore the sign of angular velocity as$\omega =+$ , and since the wheel is slowing down, therefore the angular acceleration$\alpha =-$

Part (c)

As the wheel (c) is rotating in counter-clock wise direction therefore the sign of angular velocity as $\omega =-\text{ve}$, and since the wheel is slowing down, therefore the angular acceleration$\alpha =-$

Part (d)

As the wheel (d) is rotating in clockwise direction therefore the sign of angular velocity as $\omega =+ve$, and since the wheel is speeding up, therefore the angular acceleration $\alpha =(+)\text{\hspace{0.05em}ve}$.