Uniform Circular Motion

Uniform Circular Motion What is the object being forced to do as a unbalanced force is Being applied? What was the equation for velocity? Revolution? What would be the equation For an object revolving in a circle? Period?

What do these numbers represent? Mercury . . . 88 earth days Venus . . . 225 days Earth . . . 365 days Mars . . . 685 days Jupiter . . . 12 earth years Saturn . . . 29 years Uranus . . . 84 years Neptune . . . 165 years Pluto . . .

Calculating T and Velocity What is a period, and what does it stand for? What is the period, if takes a merry go round 30 seconds to make 5 revolutions? A ball with a mass of 3.0kg is whirled by a student. The distance from the ball to the center of rotation is 4.0m. The time for one revolution is 2.0sec. What is the velocity of the ball. Zena the African warrior revolves a rope with rocks on the end of it with a radius of 1.5meters. She gets 15 revolutions in 10 seconds before she lets it go to kill a wambat. How fast was her weapon moving before she let it go?

Circular Motion B C A B: Tangent to the Circle Inertia? A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow? http://www.youtube.com/watch?v=RWeJWchXosY:// 16

Types of Weapons that use Tangential Velocity

FN v FT mg FN = mg r FT = Tension Force m F= ma Fc= m (v2 / r) mw Uniform Circular motion Is it Accelerating?

FN FN FN FN v v v v FTz FTz FTz FTz r r r r m m m m mg mg mg mg M M M M Uniform Circular motion Uniform circular motion in a horizontal plane Fc= m (v2 / r) Name 3 events as a result of a cable suddenly breaking: • Tension suddenly disappears and there is no more centripetal force • Circular motion cannot be maintained. • The rubber stopper will move with its velocity tangent to the circle at the instant the string breaks

Multipliers • How does changing a variable affect the centripetal acceleration? Manipulate the formula directly. • If aC = 15 m/s2, what if: • The mass is doubled: • The mass is halved: • The velocity is doubled: • iiii. The velocity is tripled: • v. The velocity is halved: • vi. The velocity is quartered • vii. The radius is quadrupled • viii.The radius is halved:

Multipliers How does changing a variable affect the centripetal acceleration? Manipulate the formula directly. If FC = 15 m/s2, what if: • The mass is doubled: • ii. The velocity is doubled: • iii. The velocity is halved: • iv. The radius is halved:

What is the physical meaning of the formula? Fc = m (v2 / r) Ac=V2/r V=2∏R/T T=Tt/#of revolutions • A Ball with a mass of 3.0kg is whirled overhead by a student. The distance from the ball to the center of rotation is 4.0m. • The time for one revolution is 3.0 sec. • Find the velocity of the ball • Find the centripetal acceleration • Find the centripetal force • Sketch the system, showing the magnitude and direction of the ball whirling overhead. Be sure to label all forces acting on the ball

Circular Motion Review • When we see an object carrying out circular motion, we know that there must be force acting on the object, directed towards the center of the circle. • When you look at the circular motion of a ball attached to a string, the force is provided by the tension in the string. • When the force responsible for the circular motion disappears, e.g. by cutting the string, the motion will become linear.

Sample Problem A 95 kg running back makes a turn on the football field The halfback sweeps out a path that is a portion of a circle with a radius of a 12 meters, the halfback makes a quarter turn around the circle in 2.1 seconds. Determine the speed, acceleration, and the centripetal force?

Circular Motion with Frictionbeing the Centripetal Force

Circular Motion and its Connection to Friction • When you drive your car around a corner you carry out circular motion. • In order to be able to carry out this type of motion, there must be a force present that provides the required acceleration towards the center of the circle. • This required force is provided by the friction force between the tires and the road. • But remember ….. The friction force has a maximum value, and there is a maximum speed with which you can make the turn. Required force = Mv2/r. If v increases, the friction force must increase and/or the radius must increase.

Lets Think About it? Rex Things and Doris Locked are out on a date. Rex makes a rapid right-hand turn. Doris begins sliding across the vinyl seat (that Rex had waxed and polished beforehand) and collides with Rex. To break the awkwardness of the situation, Rex and Doris begin discussing the physics of the motion that was just experienced. Rex suggests that objects which move in a circle experience an outward force. Thus, as the turn was made, Doris experienced an outward force that pushed her towards Rex. Doris disagrees, arguing that objects that move in a circle experience an inward force. In this case, according to Doris, Rex traveled in a circle due to the force of his door pushing him inward. Doris did not travel in a circle since there was no force pushing her inward; she merely continued in a straight line until she collided with Rex. Who is correct? Argue one of these two positions. When the turn is made, Doris continues in a straight-line path; this is Newton's first law of motion. Once Doris collides with Rex, there is then an unbalanced force capable of accelerating Doris towards the center center of the circle, causing the circular motion.

A 2000. kg car rounds a circular turn of radius 25 m. If the road is flat and coefficient of static friction between the tires and road is 0.70, how fast can the car go without skidding? A 2000. kg car rounds a circular turn of radius 25 m. If the road is flat and coefficient of static friction between the tires and road is 0.70, how fast can the car go without skidding? Circular Motion Problem? A 2000kg Car rounds a circular turn of radius of 25m. If the road is flat and coefficient of static friction between the tires and the road is .70. How fast can the car go without skidding

Work

Questions 2 Normal You are driving a car with constant speed around a horizontal circular track. On a piece of paper, draw a Free Body Diagram for the car. How many forces are acting on the car?A) 1 B) 2 C) 3 D) 4 E) 5 Tension 3 forces, Tension (friction), gravity and the normal force Gravity The net force on the car isA. Zero B. Pointing radially inward C. Pointing radially outward B: Force of tension is pointing inward 25

Question 3 • Davain sits on the outer rim of a merry-go-round, and Diego sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. • Diego’s velocity is: Diego Davian • (a)the same as Davian’s • (b)Faster than Davian’s • Slower than Davian’s a = V2/r (C) Diego is slower than the velocity of Davian

Summary • Uniform Circular Motion • Speed is constant • Direction is changing • Acceleration toward center a = v2 / r • Newton’s Second Law F = ma

Universal law of Gravitation • Explain Newton’s Law of Universal Gravitation. Formula?

Gravitational Pull Phenomena • Explain the inverse-square law that Newton determined directly determined the force of gravity.

Relationships

Multipliers Again? What up! • How does changing a variable affect the gravitational force? Manipulate the formula directly. • If FG = 15 N, what if: • the mass of m1 is doubled: • both masses are halved: • m1 is doubled and m2 is halved: • the distance is tripled: • the distance is halved: • the distance is quartered • the distance is quadrupled • the distance is doubled:

Problem? • Two 10.0 kg bowling balls are 50 m apart. What is the gravitational force between these two objects? What is the gravitational potential energy?

Two More Problems • The mass of the Earth is 5.98 x 1024 kg and its radius is 6.37 x 106 m. Determine the acceleration of gravity on the surface of Earth. This answer has to be in newtons. Calculate the Magnitude of the gravitational force of attraction that Earth exerts on the moon.

Uniform Circular Motion