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Chap. 7 Dynamics III: Motion in a Circle. 7.1 Uniform Circular Motion 7.2 Velocity and Acceleration in Uniform Circular Motion 7.3 Dynamics of Uniform Circular Motion 7.4* Circular Orbital 7.6 Nonuniform Circular Motion.
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Chap. 7 Dynamics III:Motion in a Circle 7.1 Uniform Circular Motion 7.2 Velocity and Acceleration in Uniform Circular Motion 7.3 Dynamics of Uniform Circular Motion 7.4* Circular Orbital 7.6 Nonuniform Circular Motion
Stop to think 7.1 P 181Stop to think 7.2 P 185Stop to think 7.3 P 190Stop to think 7.4 P 196 • Example 7.3 P 181 • Example 7.5 P 186 • Example 7.6 P 187 • Example 7.7 P 188 • Example 7.10 P 199
Uniform Circular Motion • Period • Angular Position
Angular Velocity • Average angular velocity =∆θ/∆t • Instantaneous angular velocity • The angular velocity is constant during uniform circular motion
An old-fashioned single-play vinyl record rotates 30.0 rpm . What are (a) the angular velocity in rad/s and (b) the period of the motion? • rpm: revolution per minute. 1 rpm = 2π/60 (rad)/s
Velocity in uniform circular motion The magnitude of velocity is a constant V =r dθ/dt=ωr Has only a tangential Component
The magnitude of centripetal acceleration P184 Towards center of circle
Dynamics of Uniform Circular Motiion • From the Newton’s second law, a particle of mass m moving at constant speed V around a circle of radius r must have a net force of magnitude (mV2/r) pointing toward the center of the circle
The Conical Pendulum • A small object of mass m is suspended from a string of length L. how many forces act on the object when it revolved with constant speed V in a horizontal circle?
Circular Orbits The real weight force is always directed Toward the center of the planet downwards
Tangential acceleration Change the speed Here α is angular acceleration
Dynamics of nonuniform circular motion The radial force causes the Centripetal acceleration. It makes Velocity change direction. The tangential force causes The tangential acceleration. It Makes speed change
Ex. P.47 Passenger stand inside a 16-m-diamete rotation ring.After the ring has acquired sufficient speed, It tilts into a vertical plane, as shown in the Figure At the top: At the bottom: