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 accelerat