Lecture Outline

Chapter 8

College Physics, 7th Edition

Wilson / Buffa / Lou

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Units of Chapter 8Rotational Motion and Equilibrium

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8.1 Rigid Bodies, Translations, and Rotations

A rigid body is an object or a system of particles in which the distances between particles are fixed (remain constant).

Rigid bodies only exist in a perfect, IDEAL world!

In other words, a rigid body must be solid (but not all solid bodies are rigid).

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8.1 Rigid Bodies, Translations, and Rotations

A rigid body may have either two types of motion or both:

1. Translational

2. Rotational

What’s the difference between the two?

You can combine both types of forces and that’s where we get the term ROLLING!

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8.1 Rigid Bodies, Translations, and Rotations

For an object that is rolling without slipping,

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s = rθ

a = rα

An object can roll with slipping, but none of the equations will hold when there is slipping.

8.1 Rigid Bodies, Translations, and Rotations

• A cylinder rolls on a horizontal surface without slipping. The cylinder has a radius of 12 cm and a center of mass speed of 0.10 m/s as it rolls without slipping. If it continues to travel at this speed for 2.0s, through what angle does the cylinder rotate during this time?

8.2 Torque, Equilibrium, and StabilityThe perpendicular distance from the line of force to the axis of rotation is called the lever arm or the moment arm. [symbol r, (like radius)

The product of the force and the lever arm is called the torque.

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S.I. Unit: m N

8.2 Torque, Equilibrium, and Stability

Torque in rotational motion can be thought of as the analogue of force in translational motion.

Torque (rotational) is similar to Force (linear)

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8.2 Torque, Equilibrium, and Stability

Torque is a vector or scalar????

Counterclockwise is positive, and clockwise is negative.

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8.2 Torque, Equilibrium, and Stability

• In the human body torques produced by the contraction of muscles cause some bones to rotate at joints. With the axis of rotation through the elbow joint and the muscle attached 4.0 cm from the joint, what are the magnitudes of the muscle torques for cases a and b if the muscle exerts a force of 600 N.

8.2 Torque, Equilibrium, and Stability

In order for an object to be in equilibrium, the net force on it must be zero, and the net torque on it must be zero as well.

Equilibrium means that forces and torques are in balance.

Can be at ______ or at _________ __________.

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8.2 Torque, Equilibrium, and Stability

• Two types of equilibrium: – Translational linear; forces– Rotational circular; torques

Mechanical Equilibrium

Static Equilibrium

8.2 Torque, Equilibrium, and Stability

Concurrent Forces vs. Couple

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8.2 Torque, Equilibrium, and Stability

• A picture hangs motionless on a wall. If the picture has a mass of 3.0 kg, what are the magnitudes of the tension forces in the wires?

8.2 Torque, Equilibrium, and Stability

• Three masses are suspended from a meter stick. How much mass must be suspended on the right side for the system to be in static equilibrium? [Neglect the mass of the meter stick]

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8.2 Torque, Equilibrium, and Stability

If an object is in stable equilibrium, any displacement from the equilibrium position will create a torque that tends to restore the object to equilibrium. Otherwise the equilibrium is unstable.

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8.2 Torque, Equilibrium, and Stability

Whether equilibrium is stable or unstable depends on the width of the base of support.

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