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Chapter 10: Problem 5

Is it possible to apply a counterclockwise torque to an object that's rotating clockwise? If so, how will the object's motion change? If not, why not?

Short Answer

Expert verified
Yes, it is possible to apply a counterclockwise torque to a clockwise rotating object. The effect is to slow the object's clockwise rotation. If the torque is applied until the object's angular momentum reaches zero, the object will stop rotating. If the torque is continued to be applied after this point, the object will start to rotate in the counterclockwise direction.

Step by step solution

01

Understanding Torque

Torque, represented by the Greek letter tau \(\tau\), is the rotational equivalent of force. It is determined by the equation \(\tau = rFsin(胃)\), where \(r\) is the distance from the axis of rotation to where the force is applied, \(F\) is the magnitude of the force, and \(胃\) is the angle between \(r\) and \(F\). Torque can be applied in either a clockwise or counterclockwise direction.
02

Understanding Angular Momentum

Angular momentum, represented by the letter \(L\), is the rotational equivalent of linear momentum. The direction of angular momentum is determined by the right-hand rule, which states that if you wrap your right hand around the rotation axis with your fingers pointing in the direction of rotation, your thumb points in the direction of the angular momentum vector.
03

Torque and Angular Momentum Relation

Newton's second law for rotation says that the torque on a body is equal to the time rate of change of its angular momentum. This means if a torque is applied to a body, its angular momentum will change. This change can take the form of a change in the magnitude of the angular momentum, a change in its direction, or both.
04

Applying Counterclockwise Torque

A counterclockwise torque applied to a clockwise rotating object will decrease its angular momentum in the clockwise direction. This means the object will slow down.
05

Effect on the Object's Motion

If the counterclockwise torque continues to be applied until the angular momentum reaches zero, the object will stop rotating. If the torque is continued to be applied after this point, the object will start to rotate in the counterclockwise direction. Thus, by applying a counterclockwise torque to a clockwise rotating object, it is possible to first stop the object's rotation and then make it rotate in the opposite (counterclockwise) direction.

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Most popular questions from this chapter

You're an astronaut in the first crew of a new space station. The station is shaped like a wheel 22 m in diameter, with essentially all its \(5 \times 10^{5}-\mathrm{kg}\) mass at the rim. When the crew arrives, it will be set rotating at a rate that requires an object at the rim to have radial acceleration \(g\), thereby simulating Earth's surface gravity. This will be accomplished using two small rockets, each with \(100-\mathrm{N}\) thrust, mounted on the station's rim. Your job is to determine how long to fire the rockets and the number of revolutions the station will make during the firing.

You rev your car's engine and watch the tachometer climb steadily from 1200 rpm to 5500 rpm in 2.7 s. What are (a) the engine's angular acceleration and (b) the tangential acceleration of a point on the edge of the engine's 3.5 -cm-diameter crankshaft? (c) How many revolutions does the engine make during this time?

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Four equal masses \(m\) are located at the corners of a square of side L, connected by essentially massless rods. Find the rotational inertia of this system about an axis (a) that coincides with one side and (b) that bisects two opposite sides.

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