Transcript PhysCh7.78
Chapter 7 7.1 Measuring rotational motion Rotational Quantities • Rotational motion: motion of a body that spins about an axis – Axis of rotation: the line about which the rotation occurs • Circular motion: motion of a point on a rotating object Rotational Quantities • Circular Motion – Direction is constantly changing – Described as an angle – All points (except points on the axis) move through the same angle during any time interval Circular Motion • Useful to set a reference line • Angles are measured in radians s r • s= arc length • r = radius Angular Motion • 360o = 2rad • 180o = rad (rad) 180 (deg) Angular displacement • Angular dispacement: the angle through which a point line, or body is rotated in a specified direction and about a specified axis s r • Practice: – Earth has an equatorial radius of approximately 6380km and rotates 360o every 24 h. • What is the angular displacement (in degrees) of a person standing at the equator for 1.0 h? • Convert this angular displacement to radians • What is the arc length traveled by this person? Angular speed and acceleration • Angular speed: The rate at which a body rotates about an axis, usually expressed in radians per second avg t • Angular acceleration: The time rate of change of angular speed, expressed in radians per second per second 2 1 avg t2 t1 t Angular speed and acceleration ALL POINTS ON A ROTATING RIGID OBJECT HAVE THE SAME ANGULAR SPEED AND ANGULAR ACCELERATION Rotational kinematic equations Angular kinematics • Practice – A barrel is given a downhill rolling start of 1.5 rad/s at the top of a hill. Assume a constant angular acceleration of 2.9 rad/s • If the barrel takes 11.5 s to get to the bottom of the hill, what is the final angular speed of the barrel? • What angular displacement does the barrel experience during the 11.5 s ride? Homework Assignment • Page 269: 5 - 12 Chapter 7 7.2 Tangential and Centripetal Acceleration Tangential Speed • Let us look at the relationship between angular and linear quantities. • The instantaneous linear speed of an object directed along the tangent to the object’s circular path • Tangent: the line that touches the circle at one and only one point. Tangential Speed • In order for two points at different distances to have the same angular displacement, they must travel different distances • The object with the larger radius must have a greater tangential speed Tangential Speed v t r Tangential Acceleration • The instantaneous linear acceleration of an object directed along the tangent to the object’s circular path v t t r t a t r Lets do a problem • A yo-yo has a tangential acceleration of 0.98m/s2 when it is released. The string is wound around a central shaft of radius 0.35cm. What is the angular acceleration of the yo-yo? Centripetal Acceleration • Acceleration directed toward the center of a circular path • Although an object is moving at a constant speed, it can still have an acceleration. • Velocity is a vector, which has both magnitude and DIRECTION. • In circular motion, velocity is constantly changing direction. Centripetal Acceleration • vi and vf in the figure to the right differ only in direction, not magnitude • When the time interval is very small, vf and vi will be almost parallel to each other and acceleration is directed towards the center Centripetal Acceleration ac vt 2 r a c r2 Tangential and centripetal accelerations • Summary: – The tangential component of acceleration is due to changing speed; the centripetal component of acceleration is due to changing direction • Pythagorean theorem can be used to find total acceleration and the inverse tangent function can be used to find direction What’s coming up • • • • HW: Pg 270, problems 21 - 26 Monday: Section 7.3 Wednesday: Review Friday: TEST over Chapter 7 Chapter 7 7.3: Causes of Circular Motion Causes of circular motion • When an object is in motion, the inertia of the object tends to maintain the object’s motion in a straight-line path. • In circular motion (I.e. a weight attached to a string), the string counteracts this tendency by exerting a force • This force is directed along the length of the string towards the center of the circle Force that maintains circular motion • According to Newton’s second law Fc ma c or: Fc mv t 2 r Fc mr 2 Force that maintains circular motion • REMEMBER: The force that maintains circular motion acts at right angles to the motion. • What happens to a person in a car(in terms of forces) when the car makes a sharp turn.