7.1 Angular Measure r is a distance that extends from the origin. r is the same for any point on a given circle. (like the radius!) Θ is an angle, and it changes with time. Linear Displacement…how do we calculate? Angular Displacement is VERY similar
7.1 Angular Measure Δθ = θ - θ i The unit for angular displacement is the degree. There are 360 degrees in one complete circle.
7.1 Angular Measure The arc length, s, is the distance that is traveled along the circular path. The θ is said to define the arc length. It is most convenient to measure the angle θ in radians.
7.1 Angular Measure A spectator standing at the center of a circular running track observes a runner start a practice race 256m due east of her own position. The runner runs on the track to the finish line, which is located due north of the observer’s position. What is the distance of the run?
7.1 Angular Measure A sailor sights a distance tanker ship and finds that it subtends an angle of 1.15 degrees. He knows from the shipping charts that the tanker is 150m in length. Approximately how far away is the tanker?
7.2 Angular Speed and Velocity How do we calculate speed? What’s the difference between average speed and instantaneous speed?
7.2 Angular Speed and Velocity An amusement park merry go round at its constant operational speed makes one complete rotation in 45 seconds. Two children are on horses, one at 3.0 m from the center of the ride and the other farther out at 6.0 m from the center. –What are the angular speeds of each? –What are the tangential speeds of each?
7.2 Angular Speed and Velocity the frequency is the number of revolutions (rotations) per second. [Units: Hertz] The relation of the frequency to the angular speed:
7.2 Angular Speed and Velocity A CD rotates in a player at a constant speed of 200 rpm. What are the CD’s –Frequency? –Period?
7.3 Uniform Circular Motion and Centripetal Acceleration The acceleration in uniform circular motion is called centripetal acceleration. Centripetal means “center-seeking.” Centripetal acceleration is directed inward or “into” the circle. The tangential velocity is perpendicular to the centripetal acceleration.
7.3 Uniform Circular Motion and Centripetal Acceleration A laboratory centrifuge operates at a rotational speed of 12,000 rpm. –What is the magnitude of the centripetal acceleration of a red blood cell at a radial distance of 8.00 cm from the centrifuge’s axis of rotation? –How does this acceleration compare with g?
7.3 Uniform Circular Motion and Centripetal Acceleration A ball is attached to a string is swung with uniform motion in a horizontal circle above a person’s head. If the string breaks, which of the trajectories shown on the following slide would the ball follow.
7.3 Uniform Circular Motion and Centripetal Acceleration Centripetal force is not a new individual force, but rather the cause of the centripetal acceleration. –What do I mean?? Examples?
7.3 Uniform Circular Motion and Centripetal Acceleration Suppose two masses, m 1 = 2.5 kg and m 2 = 3.5 kg are connected by two light strings and are in uniform circular motion on a horizontal frictionless surface where r 1 = 1.0 m and r 2 = 1.3 m. The tension forces acting on the masses at T 1 = 4.5 N and T 2 = 2.9 N. Find the magnitude of the centripetal acceleration.
7.3 Uniform Circular Motion and Centripetal Acceleration A 1.0 m cord is used to suspend a tetherball from the top of a pole. After being hit several times, the ball goes around the pole in uniform circular motion with a tangential speed of 1.1 m/s at an angle of 20 degrees. The force that supplies the centripetal acceleration is: –A.) the weight of the ball? –B.) a component of the tension force in the string? –C.) the total tension in the string?
7.4 Angular Acceleration A CD accelerates uniformly from rest to its operational speed of 500 rpm in 3.50 s. –What is the angular acceleration of the CD during this time? –What is the angular acceleration of the CD as its playing the song at a constant speed? –If the CD comes to a stop in 4.50 seconds, what is the angular acceleration?
7.4 Angular Acceleration A microwave oven has a 30 cm diameter rotating plate for even cooking. The plate accelerates from rest at a uniform rate of 0.87 rad/s 2 for 0.50 s before reaching its constant operational speed. –A.) How many revolutions does the plate make before reaching its operational speed? –B.) What are the operational angular speed of the plate and the operational tangential speed?
7.5 Newton’s Law of Gravitation What is Newton’s Law of Gravitation? Do you remember the video you watched last year that deals with this? –Had to do with 2 lead balls over time coming together.
7.5 Newton’s Law of Gravitation The gravitational attractions of the Sun and the moon give rise to ocean tides. It is sometimes said that since the Moon is closer to the Earth than the Sun, the Moon’s gravitational attraction is much stronger, and therefore has a greater influence on ocean tides. Is this true? –m E = 6.0 x 10 24 kg –m M = 7.4 x 10 22 kg –m S = 2.0 x 10 30 kg –r EM = 3.8 x 10 8 m –r ES = 1.5 x 10 8 km