CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS GENERAL PHYSICS LECTURE Chapter 6 CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS PhD: Nguyễn Thị Ngọc Nữ

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion 6.2 Nonuniform Circular Motion 6.3 Motion in Accelerated Frames

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion

Quick Quiz You are riding on a Ferris wheel (Fig. 6.3) that is rotating with constant speed. The car in which you are riding always maintains its correct upward orientation—it does not invert. What is the direction of your centripetal acceleration when you are at the top of the wheel? (a) upward (b) downward (c) impossible to determine. What is the direction of your centripetal acceleration when you are at the bottom of the wheel?

Quick Quiz Fig. 6.3

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion Example 1 A small object of mass m is suspended from a string of length L. The object revolves with constant speed v in a horizontal circle of radius r, as shown in Figure 6.4. (Because the string sweeps out the surface of a cone, the system is known as a conical pendulum.) Find an expression for v.

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion Example 1

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion Example 2 A 1 500-kg car moving on a flat, horizontal road negotiates a curve, as shown in Figure 6.5. If the radius of the curve is 35.0 m and the coefficient of static friction between the tires and dry pavement is 0.500, find the maximum speed the car can have and still make the turn successfully.

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion Example 2

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion Example 3 A pilot of mass m in a jet aircraft executes a loop-the-loop, as shown in Figure 6.7a. In this maneuver, the aircraft moves in a vertical circle of radius 2.70 km at a constant speed of 225 m/s. Determine the force exerted by the seat on the pilot (A) at the bottom of the loop and (B) at the top of the loop.

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS Example 3

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS Example 3

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion Problem A 4.00-kg object is attached to a vertical rod by two strings, as in Figure P6.11. The object rotates in a horizontal circle at constant speed 6.00 m/s. Find the tension in (a) the upper string and (b) the lower string.

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.1 Newton’s Second Law Applied to Uniform Circular Motion Problem Figure P6.11

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.2 Nonuniform Circular Motion

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.2 Nonuniform Circular Motion Quick Quiz 1 Which of the following is impossible for a car moving in a circular path? the car has tangential acceleration but no centripetal acceleration. the car has centripetal acceleration but no tangential acceleration. the car has both centripetal acceleration and tangential acceleration.

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.2 Nonuniform Circular Motion Quick Quiz 2 A bead slides freely along a horizontal, curved wire at constant speed, as shown in Figure. Draw the vectors representing the force exerted by the wire on the bead at points A, B, and C.

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.2 Nonuniform Circular Motion Quick Quiz 3 In Figure, the bead speeds up with constant tangential acceleration as it moves toward the right. Draw the vectors representing the force on the bead at points A, B, and C.

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.2 Nonuniform Circular Motion Example A small sphere of mass m is attached to the end of a cord of length R and set into motion in a vertical circle about a fixed point O, as illustrated in Figure 6.10. Determine the tension in the cord at any instant when the speed of the sphere is v and the cord makes an angle q with the vertical.

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.2 Nonuniform Circular Motion Example

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.2 Nonuniform Circular Motion Problem A pail of water is rotated in a vertical circle of radius 1.00 m. What is the minimum speed of the pail at the top of the circle if no water is to spill out?

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.2 Nonuniform Circular Motion Problem

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.3 Motion in Accelerated Frames

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.3 Motion in Accelerated Frames

CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS 6.3 Motion in Accelerated Frames