Chapter 17, Problem 1PLA

To determine

The equation for the rotational equivalent of Newton’s second law and state the rotational quantities that are analogous to linear quantities.

Answer to Problem 1PLA

The equation for the rotational equivalent of Newton’s second law is $\tau =I\alpha$.

Explanation of Solution

The rotation equivalent of Newton’s second law is the equation of torque.

Write the equation for torque

    $\tau =I\alpha$        (I)

Here, $\tau$ is the torque, $I$ is the moment of inertia and $\alpha$ is the angular acceleration.

In equation (I),

The rotational quantity $\tau$ is analogous to mass $F$ in Newton’s second law, $F=ma$.

The rotational quantity $I$ is analogous to mass $m$ in Newton’s second law, $F=ma$.

The rotational quantity $\alpha$ is analogous to mass $a$ in Newton’s second law, $F=ma$.

Conclusion:

The equation for the rotational equivalent of Newton’s second lawis $\tau =I\alpha$.