Chapter 8: Dynamics II: Motion in a Plane

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Chapter 8: Dynamics II: Motion in a Plane
8.2 Velocity and Acceleration in Uniform Circular Motion 8.3 Dynamics of Uniform Circular Motion 8.7 Nonuniform Circular Motion

Stop to think 8. 2. P 214 Stop to think 8. 3. P 219 Stop to think 8. 4
Stop to think 8.2 P 214 Stop to think 8.3 P 219 Stop to think 8.4 P 226 Stop to think 8.5 P 228 Example 8.3 P215 Example 8.5 P217 Example 8.6 P218 Example 8.7 P227

Velocity and Acceleration in Uniform Circular Motion

Dynamics of Uniform Circular Motion
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

Ex. 8.3 Spinning in a circle An Energetic father places his 20 Kg child on a 5.0Kg cart to which a 2.0-m-long rope is attached. He then holds the end of the rope and spins the cart and child around in a circle, keeping the rope parallel to the ground. If the tension in the rope is 100N, how many revolutions per minute (rpm) does the cart make?

The Conical Pendulum

Problem 46: Mass m1 on the frictionless table is connected by a string through a hole in the table to a hanging mass m2. With what speed must m1 rotate in a circle of radius r if m2 is to remain hanging at rest? If m2 remains hanging at rest T-m2·g=0 (2) For m1, N = m1·g T =m1 V2 /r

A roller coaster car going around a vertical loop-the loop of radius r
A roller coaster car going around a vertical loop-the loop of radius r. We’ll assume that the motion makes a complete circle and not worry about the entrance to and exit from the loop. Why doesn’t the car fall off at the top of the circle

Nonuniform Circular Motion

Problem 8.62, A small ball rolls around a horizontal circle at height y inside a frictionless hemispherical bowl of radius R., find an expression for the ball’s angular velocity in terms of R, y, g