Which equation expresses the rotational analog to Newton's second law?

Which equation expresses the rotational analog to Newton's second law?

• A. T_net = I * Alpha
• B. F_net = m a
• C. L = r m v
• D. Tau = F r

Answer: (A)

The main idea is that rotational motion has a counterpart to force driving acceleration: torque acts to change rotation, and the resistance to that change is the distribution of mass, captured by the moment of inertia. The rotational analog to Newton's second law is that the net torque about the axis equals the moment of inertia times the angular acceleration: T_net = I α. Here T_net is the total torque, I is the moment of inertia, and α is the angular acceleration. This tells you how quickly the rotation speeds up or slows down under a given twisting force, and how that rate depends on how the mass is spread relative to the axis. Think of torque as the rotational push that causes angular speed to change, just as force causes linear speed to change. The moment of inertia plays the role mass plays in straight-line motion: larger I means the same torque produces a smaller angular acceleration. If I is constant, the relation simplifies to τ = I α, tying the applied twist directly to how fast the rotation speeds up. For reference, torque by itself is defined as F times the lever arm, which is a basic way to quantify rotation, but it doesn’t by itself describe how rotation evolves in time unless you connect it to the angular acceleration via the moment of inertia. And angular momentum concepts, L = I ω and τ = dL/dt, reinforce the same link between torque and changes in rotational motion.

The main idea is that rotational motion has a counterpart to force driving acceleration: torque acts to change rotation, and the resistance to that change is the distribution of mass, captured by the moment of inertia. The rotational analog to Newton's second law is that the net torque about the axis equals the moment of inertia times the angular acceleration: T_net = I α. Here T_net is the total torque, I is the moment of inertia, and α is the angular acceleration. This tells you how quickly the rotation speeds up or slows down under a given twisting force, and how that rate depends on how the mass is spread relative to the axis.

Think of torque as the rotational push that causes angular speed to change, just as force causes linear speed to change. The moment of inertia plays the role mass plays in straight-line motion: larger I means the same torque produces a smaller angular acceleration. If I is constant, the relation simplifies to τ = I α, tying the applied twist directly to how fast the rotation speeds up.

For reference, torque by itself is defined as F times the lever arm, which is a basic way to quantify rotation, but it doesn’t by itself describe how rotation evolves in time unless you connect it to the angular acceleration via the moment of inertia. And angular momentum concepts, L = I ω and τ = dL/dt, reinforce the same link between torque and changes in rotational motion.