N·m

Definition

N·m, or Newton-meter, is a unit of torque or rotational force in the International System of Units (SI). It represents the product of force (in newtons) and the perpendicular distance (in meters) from the axis of rotation to the line of action of the force, and is used to quantify the rotational effect of a force.

5 Must Know Facts For Your Next Test

1. N·m is used to quantify the rotational effect of a force, which is important in understanding the dynamics of rotating systems.
2. The formula for torque is $\tau = r \times F$, where $\tau$ is the torque, $r$ is the perpendicular distance from the axis of rotation to the line of action of the force, and $F$ is the applied force.
3. Torque is a vector quantity, meaning it has both magnitude and direction, and the direction is determined by the right-hand rule.
4. In the context of Newton's Second Law for Rotation, the net torque acting on a rotating object is equal to the product of the object's moment of inertia and its angular acceleration.
5. The SI unit of moment of inertia is kg·m², which, when multiplied by the angular acceleration in rad/s², gives the torque in N·m.

Review Questions

• Explain how the N·m unit is used to quantify the rotational effect of a force.
  • The N·m unit is used to quantify the rotational effect of a force because it represents the product of the force (in newtons) and the perpendicular distance (in meters) from the axis of rotation to the line of action of the force. This combination of force and distance determines the magnitude of the torque, which is the rotational equivalent of linear force. Torque is what causes an object to rotate around an axis, and the N·m unit allows us to measure the strength of this rotational effect.
• Describe how the N·m unit is used in the context of Newton's Second Law for Rotation.
  • In the context of Newton's Second Law for Rotation, the N·m unit is used to represent the net torque acting on a rotating object. The formula for Newton's Second Law for Rotation is $\tau_{net} = I \alpha$, where $\tau_{net}$ is the net torque (in N·m), $I$ is the object's moment of inertia (in kg·m²), and $\alpha$ is the object's angular acceleration (in rad/s²). This equation shows that the net torque, measured in N·m, is the driving force that causes an object to undergo angular acceleration, which is a key concept in understanding the rotational dynamics of a system.
• Analyze how the N·m unit is related to the concept of work in the context of rotational motion.
  • The N·m unit is also related to the concept of work in the context of rotational motion. Work done on a rotating object is equal to the product of the torque (in N·m) and the angular displacement (in radians). This relationship is expressed as $W = \tau \theta$, where $W$ is the work done, $\tau$ is the torque, and $\theta$ is the angular displacement. The N·m unit, as a measure of torque, is therefore a crucial component in understanding the energy transfers and transformations that occur in rotational systems. By analyzing the work done, as measured in N·m, you can gain insights into the efficiency and dynamics of rotating objects and mechanisms.

Related terms

Torque: Torque is the rotational equivalent of linear force, and is the product of a force and the perpendicular distance from the axis of rotation to the line of action of the force.

Rotational Dynamics: Rotational dynamics is the study of the motion of objects that are rotating or spinning around an axis, and the forces that cause or affect this motion.

Angular Acceleration: Angular acceleration is the rate of change of angular velocity, and is measured in radians per second squared (rad/s²).