Dynamics: Forces. Lecture 7. Chapter 5. Course website:

Transcription

1 Lecture 7 Chapter 5 Dynamics: Forces Course website:

2 Today we are going to discuss: Chapter 5: Some leftovers from rotational motion Ch.4 Force, Mass: Section 5.1 Weight the Force of Gravity; and the Normal Force/Tension: Section

3 Rotational Kinematic Quantities (Review) Definition of radians v tan a tan Angular velocity Relationship between tangential and angular velocity Angular acceleration But it is not the whole story about accelerations! Relationship between tangential and angular acceleration Tangential acceleration a tan is not enough to describe all changes in v tan! PHYS.1410 Lecture 6 Danylov

4 Accelerations (two servants of a king) ; v tan a tan results from a change in the magnitude of v tan Tangential acceleration a tan is always tangent to the circle. Finally, any object that is undergoing circular motion experiences two accelerations: centripetal and tangential. Total acceleration: a a R (centripetal acceleration) results from a change in the direction of v tan 2 2 total a t an ar atotal at an ar Centripetal acceleration a R always points toward the center of the circle. a total a R a R a tan r v tan a R In uniform circular motion (=const), although the speed is constant, there is a centripetal acceleration because the direction of the velocity vector is always changing. PHYS.1410 Lecture 6 Danylov

5 Uniform circular motion =const A particle moves with uniform circular motion if its angular velocity is constant. The time interval to complete one revolution is called the period, T. The period T is related to the speed v: In this case, as the particle goes around a circle one time, its angular displacement is 2 during one period. Then, the angular velocity is related to the period of the motion: d dt 2 t T PHYS.1410 Lecture 6 Danylov

6 ConcepTest Car on a curve A car is traveling around a curve at a steady 45 mph. Is the car accelerating? A) Yes B) No There is a Centripetal acceleration

7 ConcepTest Car on a curve A car is traveling around a curve at a steady 45 mph. Which vector shows the direction of the car s acceleration? There is a Centripetal acceleration pointing toward the center

8 ConcepTest Car on a curve A car is slowing down as it drives over a circular hill. Which of these is the acceleration vector at the highest point? Acceleration (slowing down) of changing speed a total a tan a v tan R Acceleration of changing direction v tan

9 Lecture 7 Chapter 5 Dynamics: Forces and Newton s Laws of Motion Course website:

10 Transition from Kinematics to Dynamics It s time to complicate life In Kinematics we studied HOW things move Motion Forces Now in Dynamics we will study WHY things move Motion Forces

11 Force A force was introduced to describe interactions between two objects push A force is a push or pull pull Force has magnitude and direction: VECTOR! To quantify a push or pull, we need to specify both magnitude and a direction. An object at rest needs a force to get it moving A moving object needs a force to change its velocity

12 There are two types of forces The bat must touch the ball to hit it. Contact forces: forces that act on an object by touching it at a point of contact. Frictional Force Tension Force Normal Force Spring Force Non-contact forces (Long-range forces): forces that act on an object without physical contact (gravity). Gravity Electric force Magnetic force

13 The Major Forces

14 Spring Force The pull of a planet on an object near the surface is called the gravitational force. It comes from the entire planet A spring can either push (when compressed) or pull (when stretched). The gravitational force pulls the cat down Gravity acts on all objects, whether moving or at rest. The gravitational force vector always points vertically downward.

15 Normal Force When an object sits on a table, the table surface exerts an upward contact force on the object. This pushing force is directed perpendicular to the surface, and thus is called the normal force. Always perpendicular A table is made of atoms joined together by molecular bonds which can be modeled as springs. Normal force is a result of many molecular springs being compressed ever so slightly. End of the lecture

16 Friction Force When an object slides along a surface, the surface can exert a contact force which opposes the motion. This is called kinetic friction. Static friction is the contact force that keeps an object stuck on a surface, and prevents relative motion. The kinetic friction force is directed tangent to the surface, and opposite to the velocity of the object relative to the surface. Kinetic friction tends to slow down the sliding motion of an object in contact with a surface. The static friction force is directed tangent to the surface. Static friction points opposite the direction in which the object would move if there were no static friction.

17 Tension Force When a string or rope or wire pulls on an object, it exerts a contact force called the tension force. The tension force is in the direction of the string or rope.

18 Thank you