3.

1: uniform circular motion - motion that occurs when an object has constant speed and constant radius -also occurs if only part of the circle (an arc) is covered. centripetal acceleration - instantaneous acceleration directed toward the centre of the circle In uniform circular motion, the speed of the object remains constant, but the velocity vector changes because its direction changes. -radius of the path also remains constant -the instantaneous position vector (also called the radius vector) is perpendicular to the velocity vector - the velocity vectors are tangent to the circle. -an object travelling at a constant speed is undergoing acceleration if the direction of the velocity is changing. -in uniform circular motion is called centripetal acceleration. - the direction of the centripetal acceleration is toward the centre of the circle - the direction of the acceleration is the same as the direction of the change of velocity -the centripetal acceleration and the instantaneous velocity are perpendicular to each other. Equation: the speed of an object in circular motion increases at a constant radius, the direction of the velocity changes more quickly requiring a larger acceleration; as the radius becomes larger (at a constant speed), the direction changes more slowly, meaning a smaller acceleration. summary: Uniform circular motion is motion at a constant speed in a circle or part of a circle with a constant radius. Centripetal acceleration is the acceleration toward the centre of the circular path of an object travelling in a circle or part of a circle. Vector subtractions of position and velocity vectors can be used to derive the equations for centripetal acceleration. 3.2: According to Newtons second law of motion, centripetal acceleration is the result of a net force acting in the direction of the acceleration (toward the centre of the circle) and perpendicular to the instantaneous velocity vector. -Since centripetal acceleration is directed toward the centre of the circle, the net force must also be directed toward the centre of the circle. -F is the magnitude of the net force that causes the circular motion vold = 1.4vnew <- circular vs. clothoid loop -centripetal force net force that causes centripetal acceleration -centripetal force is not a separate force of nature; rather it is a net force that can be a single force (such as gravity) or a combination of forces (such as gravity and a normal force). -centrifugal force fictitious force in a rotating (accelerating) frame of reference -Since an object in circular motion is accelerating, any motion observed from that object must exhibit properties of a noninertial frame of reference. -for example, the forces you feel when you are the passenger in a car during a left turn. You feel as if your right shoulder is being pushed against the passenger-side door. From Earths frame of reference (the inertial frame),

this force that you feel can be explained by Newtons first law of motion: you tend to maintain your initial velocity (in both magnitude and direction).When the car you are riding in goes left, you tend to go straight, but the car door pushes on you and causes you to go in a circular path along with the car. Thus, there is a centripetal force to the left on your body -Consider the same situation from the accelerating frame of reference of the car. You feel as if something is pushing you toward the outside of the circle. (centrifugal) -Since the passenger is stationary (and remains so) in the rotating frame, the sum of the forces in that frame is zero. - centrifuge - rapidly-rotating device used for separating substances and training astronauts; practical application ex.,, Test tubes containing samples are rotated at high frequencies; some centrifuges have frequencies higher than 1100 Hz. A dense cell or molecule near the top of a tube at position A tends to continue moving at a constant speed in a straight line (if we neglect fluid friction due to the surrounding liquid). This motion carries the cell toward the bottom of the tube at position B. Relative to the rotating tube, the cell is moving away from the centre of the circle and is settling out. Relative to Earths frame of reference, the cell is following Newtons first law of motion as the tube experiences an acceleration toward the centre of the centrifuge Another rotating noninertial frame of reference is Earths surface. As Earth rotates daily on its axis, the effects of the centrifugal acceleration on objects at the surface are very small; nonetheless, they do exist. For example, if you were to drop a ball at the equator, the ball would fall straight toward Earths centre because of the force of gravity. However, relative to Earths rotating frame of reference, there is also a centrifugal force directed away from Earths centre. (This is Newtons first law of motion in action; you feel a similar, though much greater effect when travelling at a high speed over the hill of a roller coaster track.) Thus, the net force on the ball in Earths rotating frame is less than the force of gravity in a nonrotating frame of reference. -The acceleration of the ball at the equator is about 0.34% less than the acceleration due to gravity alone. The magnitude of the centrifugal force is a maximum at the equator, and decreases to zero at the Poles. -Coriolis force - fictitious force that acts perpendicular to the velocity of an object in a rotating frame of reference -this fictitious force acts on objects that are in motion relative to the rotating frame. For most objects moving at Earths surface, the effect of the Coriolis force is not noticeable. However, for objects that move very quickly or for a very long time, the effect is important. For example, the Coriolis force is responsible for the rotation of many weather patterns, such as the low-pressure systems that rotate counter clockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere summary: The net force acting on an object in uniform circular motion acts toward the centre of the circle. (This force is sometimes called the centripetal force, although it is always just gravity, the normal force, or another force that you know already.) The magnitude of the net force can be calculated by combining Newtons second law equation with the equations for centripetal acceleration. The frame of reference of an object moving in a circle is a noninertial frame of reference. Centrifugal force is a fictitious force used to explain the forces observed in a rotating frame of reference. Centrifuges apply the principles of Newtons first law of motion and centrifugal force. The Coriolis force is a fictitious force used to explain particles moving in a rotating frame of reference.