HCI Moments Notes

Hwa Chong Institution Sec 4 Physics 1 Name: ___________________________________________ Class: __________ Date: ____________ Sec 4 Physics Topic 25 Rotational Motion and Torque Essential questions 1. How does a force cause a turning effect on objects? 2. How can we use moments to help us understand the stability of objects? 25.1 CIRCULAR MOTION Observe the following picture. Two bugs are standing on a spinning disc with one bug at half the disc’s radius and one at its full radius. Does the bug at the edge of the disc travel twice as fast? Do they have the same rate of spin? Rotational speed (sometimes called angular speed) involves the number of rotations per unit time. All parts of the rotating disc above turn about the axis of rotation in the same amount of time. All parts have the same rate of rotation, or same num ber of rotations per unit time or same angular speed. It is common to express the rate of rotation in revolutions per minute (RPM). The SI unit is radians per second (rad s-1). Tangential speed, unlike rotational speed, depends on the radial distance from the centre of rotation. Tangential speed and rotational speed are related. Have you ever ridden on a big, round, rotating platform in an amusement park? The faster it turns, the faster your tangential speed. In fact, the tangential speed is directly proportional to rotational speed at any fixed distance from the axis of rotation. vr  where  (Greek letter omega) is the angular speed and v is tangential speed.

Hwa Chong Institution Sec 4 Physics 2 Table of types of speed / velocity Type Definition SI units Linear Speed in a single direction ms-1 Tangential Speed parallel to the tangent of a circle / trajectory. ms-1 Radial (Centripetal) Speed directed toward or away along a radial direction. ms-1 Angular (Rotational) Rate of rotation. rad s-1 When tangential speed undergoes change, we speak of a tangential acceleration. Any change in tangential speed indicates an acceleration parallel to the tangential motion. You should recall in the Topic 2-D Kinematics, we have already discussed another acceleration – one that is directed toward the centre of curvature – centripetal a cceleration. To prevent “information overload”, we will not discuss tangential acceleration here. Check your understanding An object is rotating at 2000 rpm, how fast is it rotating in rad s-1?      1 2000 rev 2 rad/rev2000 rpm 60 s/min 209 rad s     What is the theoretical maximum rate of rotation for an object of radius 1 m? The maximum speed limited by the speed of light and hence, the tangential speed at the outermost radius cannot exceed this limit.  . . 8 81 3 00 10 1 3 00 10 rad s 3 000 000 000 rpm vr          When an object is rotating, does it exhibit radial motion? If yes, give an example. In uniform circular motion, there is no radial velocity (though there is a radial/centripetal acceleration). For an object to exhibit radial velocity, the object must be either spiralling inward to or outward from the centre of the circular motion.

Hwa Chong Institution Sec 4 Physics 3 25.2 ROTATIONAL INERTIA Just as an object at rest tends to stay at rest and an object in motion tends to remain moving unchangingly in a straight line, an object rotating about an axis tends to remain rotating about the same axis unless interfered with by some external influence . The property of an object to resist changes to resist its state of motion is called rotational inertia or more commonly, the moment of inertia. Translational motion Inertia Rotational motion Moment of inertia Unlike inertia which depends solely on mass, the moment of inertia also depends on how the mass is distributed about the axis of rotation. When the mass is distributed further from the axis of rotation, the greater is its moment of inertia and consequently harder to rotate. Check your understanding Which should roll faster, a solid cylinder or a loop? Ans: A solid cylinder rolls down an incline faster than a loop. A loop has greater rotational inertia relative to its mass than a cylinder does. (Above): Moment of inertia depends on the distribution of mass relative to the axis of rotation. (left): The ten dency of the pole to resist rotation aids the acrobat. (Far right): Short legs have less moment of inertia than long legs. An animal with short legs has a quicker stride than people with long legs. (Right): You bend your legs when you run to reduce moment of inertia.

Hwa Chong Institution Sec 4 Physics 4 Rotational inertia of various objects, each of mass m, about indicated axes. Example 1 A pencil (above) has different moments of inertia about different rotational axes. On which axis would it be hardest to rotate? Which is the easiest? 25.3 TORQUE (MOMENT OF A FORCE) A force has the ability to 1 cause an object to accelerate. 2 cause an object to turn. (turn faster or slower or even change direction of turning) 3 change the shape of an object. (deformation) In this chapter, we shall focus our attention on one particular effect, that is, the turning effect of a force. Some examples of turning effects are shown in the pictures below.

Hwa Chong Institution Sec 4 Physics 5 Turning effects in engineering Strictly speaking, it is not a force that changes the state of rotational motion but a torque (or moment). Mathematically, dF   Torque, denoted by Greek letter 𝜏 (pronounced tau), is a vector quantity.  The SI unit for torque is Nm (Newton-meter). A torque is the rotational counterpart of a force. Force tends to change the translational motion of objects; torque twists or changes the state of rotation of things. If you want to make a stationary object move or a moving object to change speed, apply force. If you want to make a stationary object rotate or a rotating object change rotational speed, apply torque. Perpendicular distance The first step in the calculation of moments is to identify the perpendicular distance (which is also the shortest distance) from the force to the pivot (point of rotation). Let’s look at some examples and see if you can identify the perpendicular distances. (Left) Tower Bridge, London. The two halves of the roadway, each about 50m long and 1000 tons, are raised by the turning effect or moment of forces produced by hydraulic machinery. Definition: The torque (or moment of a force) is the product of the force and the perpendicular distance of the pivot from the line of action of the force.

Hwa Chong Institution Sec 4 Physics 6 Example 2 Draw a line to represent the perpendicular distance from the pivot to the line of action of the force. Check your understanding (i) Draw the perpendicular distance from the pivot to the line of action of the force for each of the six forces. (ii) Which of the forces would not result in a torque about the pivot? (iii) When the line of action of the force intersects the pivot point, then there is no torque about the pivot. Clockwise and anti-clockwise moments There are two ways to turn an object: (i) a clockwise rotation; (ii) an anti-clockwise rotation. (anti-clockwise is also called counter-clockwise) Important: The direction of the torque is neither clockwise nor anti -clockwise. The discussion of the torque’s direction requires advanced mathematics that is beyond the scope of the syllabus. F Showing only F1 and F5. Figure the rest on your own.

Hwa Chong Institution Sec 4 Physics 7 Example 3 The two pictures below show two different ways of pedalling a bicycle. The applied force is 20 N and the length between the axle A and the pedal P is 30 cm. Calculate the moments for each of the situation. Which way is easier to pedal?