Question

which of the following motions should be correctly analyzed using the torque version of Newton's 2nd law? Circle all that apply.

a. a car slows to a stop as it approaches a traffic light on a straight road.

b. a car travels around a circular path.

c. a car travels around a circular path on a banked road.

d. the tires of a car spin at a constant rate as the car goes around a curve.

Answer 1

Only option (d) describes a motion that involves torque. So only option (d) is correct.

Option (a) describes a motion in which a car travelling in a rectilinear manner,stops. There is no rotation involved and therefore no torque.

Option (b) and see describe circular motion. In circular motion,there is always a radial component of the acceleration even when the magnitude of the velocity is constant, because the direction of motion is constantly changing. This radial acceleration results in a radial force called the centripetal force. But the motion of the car on a circular psth, is always perpendicular to the centripetal force. So there cross product is zero and therefore torque is zero.

Only option (d) describes a case of rotational motion of the tires of the car. There is alwaya torque associated with the rotational motion. So only motion described by option (d) cam be analysed by torque version of Newton's second law

i.e.

Where I is the moment of inertia and  is the angular acceleration.