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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

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**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

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**Velocity and Acceleration in Uniform Circular Motion**

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**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

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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?

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The Conical Pendulum

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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

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**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

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**Nonuniform Circular Motion**

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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

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Gravity is 9.8 or ~10 m/s 2 If dropped from rest: y = -½ gt 2.

Gravity is 9.8 or ~10 m/s 2 If dropped from rest: y = -½ gt 2.

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