Physics · System Of Particles And Rotational Motion · NEET
No. Force changes linear (straight-line) motion; torque changes rotational motion. NCERT explains it with a door: the SAME push opens the door easily when applied near the outer edge, but barely moves it near the hinge. The force is equal in both cases, yet the turning effect is different. That turning effect is torque, and it depends on WHERE and in WHICH DIRECTION the force acts, not just how big the force is.
Because torque = force x lever arm. The lever arm is the perpendicular distance from the axis to the line of the force. Push far from the hinge and you get a long lever arm, so a big turning effect. Push close to the hinge and the lever arm is short, so almost no turning. This is exactly why door handles are placed at the edge farthest from the hinges, and why a longer spanner loosens a bolt more easily.
theta is the angle between the position vector r (from axis to the point where force acts) and the force F. Only the part of the force that acts ACROSS r (perpendicular, F sin theta) produces turning. If you pull straight along r (theta = 0 or 180 degrees), sin theta = 0, so torque is zero even though the force is large. Maximum torque comes at theta = 90 degrees, where you push exactly perpendicular to the arm.
Torque is a vector. Its direction is given by tau = r x F using the right-hand rule: point your fingers along r, curl them toward F, and your thumb points along tau. This direction is perpendicular to the plane containing r and F. For NEET, remember reversing F reverses the direction of tau, and the SI unit is newton metre (N m).
Three cases from NCERT: (1) r = 0, the force acts at the axis itself; (2) F = 0, no force; or (3) theta = 0 degrees or 180 degrees, the line of action of the force passes through the axis (force is along r). So a force whose line of action passes through the pivot produces NO torque, no matter how large it is. This is a favourite NEET trap.
Yes, they mean the same thing. NCERT titles this section Moment of force (Torque). Moment of a force about a point = tau = r x F. In equilibrium problems (rods, levers, see-saws) it is usually called moment; in rotational dynamics it is usually called torque. Both are measured in N m and both mean the turning effect of a force.
The torque about the origin when a force 3 j-hat N acts on a particle whose position vector is 2 k-hat m is:
Which of the following statements are correct? (a) The centre of mass of a body always coincides with its centre of gravity. (b) The centre of mass is the point where the total gravitational torque on the body is zero. (c) A couple on a body produces both translational and rotational motion. (d) Mechanical advantage greater than one means a small effort can lift a large load.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The SI unit of torque is the newton metre (N m). Note this looks like the unit of energy (joule = N m), but torque is a vector quantity and is NOT energy, so we never write it as joule.
Torque is tau = r x F (vector form). Its magnitude is tau = r F sin(theta), where theta is the angle between the position vector r and the force F. You can also write it as tau = F x d, where d = r sin(theta) is the perpendicular distance from the axis to the line of the force (the lever arm).
Torque points perpendicular to the plane containing r and F, given by the right-hand rule of the cross product r x F. Curl the fingers of your right hand from r toward F; your thumb points in the direction of torque. Reversing the force reverses the direction of the torque.
Torque is maximum when the force is perpendicular to the arm (theta = 90 degrees, sin theta = 1). Torque is zero when the force acts along the arm (theta = 0 or 180 degrees) or when the line of action of the force passes through the axis, or when r = 0.
Torque is the foundation of the whole rotational motion chapter: equilibrium of rigid bodies, principle of moments, angular momentum (tau = dL/dt) and rotational dynamics (tau = I alpha). NEET regularly asks a direct r x F calculation and lever/balance problems, so mastering torque here makes the later topics far easier.
