rotational motion chapter 7 rotational motion motion about an axis of rotation. a record turntable...

Rotational Motion Chapter 7

Rotational Motion Motion about an axis of rotation. A record turntable rotates; A bug sitting on the record revolves around the axis and is said to undergo circular motion.

Particles in the rings of Saturn rotate using circular motion.

Spin cycle of washer The spin cycle of your washer works on the principle that your clothing is forced to follow a circular path, but the water in the clothing escapes through holes in the side of the drum, not following a circular path.

Measuring rotational motion: You have probably already encountered the radian, the measure of angular displacement: Angle whose arc length = its radius = s/r is anglular in radians, s is arc length, r is radius Converting to degrees: 2 (rad) = 360 (deg)

Just like linear displacement, the direction matters. Conventionally, rotation is.. Positive when Counterclockwise Negative when Clockwise Lets do the problem on P246. H/W P247 Q1-4

P247 answers 1. 1.7 rad 2.Pi rad, 1.2 m 3. 0.34 rad 4.2.5 rad,6.4m, - 320 , 1.1m

Angular velocity: Think of it as how quickly something is turning A unit that is often used is revolutions per minute (RPM) Old records spun at 33.3, 45 or 76 RPM Car engines often run most efficiently at about 2500 RPM and produce the maximum power about 4500rpm Most electric motors spin at a multiple or sub multiple of 3600RPM or 60 revolutions/sec

Angular velocity (speed) Just like motion in a straight line, after displacement comes speed . Angular speed is the rate of change of angular displacement = /t Units are rad/s Lets do problem on P248 H/W P248 Q1-4

P248 answers 1.29 rad/s 2.2.2 rad/s 3.7.3 X 10- 5 rad/s 4.A) 0.23 rad/s b) 0.24 rad c) -6.3 rad/s d) 0.75s

Angular acceleration: Think of it as how quickly a rotating object speeds up or slows down. The angular acceleration of the earth is High:Low: Zero The angular acceleration of a bicycle wheel is pulling away from a stop High:Low:Zero The angular acceleration of a motorcycle doing a constant 150mphis High:Low:Zero The angular acceleration of a motorbike wheel pulling away from a race start is High:Low: Zero

Angular acceleration Rate of change of angular velocity, = f i t Units are rad/s 2 Lets do Problem on P249 H/W P. 250 Q1,2,3

P250 Answers 1.4.3rad/s 2 2.1.3rad/s 2 3.a)17rad/s 2 b)0.038rad/s c)-6.3 rad/s 2

Angular kinematic equations: f = i + t = i t + 1/2 t 2 f 2 = i 2 + 2 ( f - i ) =1/2 ( i + f ) t

Answers to P 252 9.0 rad/s 25 rad/s 2 15 rad/s 31 rad/s 0.89 rad/s

Section review: 1.0.44rad, 0.61 rad, 2.23 rad, 4.7 rad 2.-1.0 rad 3.0.314 rad/s 4.0.20 rad/s 2 5. 0.70 rad/s Page 269 Q10: 0.042rad/s, Q11a) 821rad/s 2, b) 4.2 X10 3 rad

Remember the strategy: Write down the givens and unknown. Find the equation that has all the givens and unknown and nothing else. If necessary, rearrange the equation to find the unknown and then substitute to solve.

Tangential Speed (7.2) Speed of an object (m/s) traveling in a circle is called Tangential Speed because the direction of motion is always in a tangent to the circle.

Tangential speed: Tangential speed would be important to find out how fast a point on the earth is travelling in a given time etc v t (m/s) = r

Tangential Acceleration: The rate of change of tangential speed. It is the linear acceleration of a point undergoing angular acceleration: a t (m/s 2 ) = r

Centripetal acceleration: Acceleration directed toward the center of a circle that an object undergoing circular motion must experience. (Note spinning cup with water in it) a c = v t 2 / r a c = r 2

H/W : P255 1-4, P256 1-3, P258 1-5 P250 1.8m/s 6.9 m/s 9.2 m/s 3.6 m/s, 15 rad/s, 29m/s, 1.3m P256: 2.11 m/s 2, 0.18m/s 2, 1.0m/s 2

P258 answers: 3.0m/s 2 250m/s 2 1.5m/s, 1.0rad/s 12.6m/s 2 84m/s 2

Centripetal force: In order for an object to travel in a circle, something must provide a force that is directed at all times toward the center of the circle. This force is called CENTRIPETAL FORCE. For a car going around the corner, the force is provided by the ______. For a stone being twirled in a slingshot it is provided by the _______. For clothes in the spin cycle it is provided by______

For the moon traveling around the earth it is provided by _______. For the earth traveling around the sun it is provided by _______. Can you think of any other objects that undergo circular motion and identify what provides the centripetal force?

Demonstration The object on the left travels with inertia, while the object on the right is caused to travel in a circle by the wooden block. Centripetal force is applied.

Calculating Centripetal Force

Inertia should cause the car to continue in the direction in which it was traveling. What causes it to travel in a circular direction? What applies the centripetal force?

If you let go, youll be like Mary Poppins and fly off the Merry- go-Round.

You do not fly straight outward. Instead you follow tangential motion, and continue in a straight line from the point where the circular motion ends.

As usual, there is a formula: (From F=ma) F c = mv t 2 / r F c = mr 2 Homework: P261 Q1-5

Newtons universal law of gravitation There is an attractive force between any two masses or particles in the universe F = - G m 1 m 2 r 2 Where G is the universal gravitational constant, m is each mass in kg, and r is the distance separating their centers of mass G = 6.67 X 10 -11 N m 2 / kg 2

P265 1-3 top of page And Section review Keep in mind that, for an orbiting body, centripetal force = gravitational force.

Speed of an orbiting satellite: V s = (G M c /r) 1/2 Where M c is central mass, r is the total distance from center of rotation.

Escape Velocity: There is a speed at which an object shot straight up from a planet will have enough energy to escape the gravitational field of the planet. V esc = ( 2MG/R) 1/2 M is the mass of the planet.

g, the acceleration due to gravity on any planet surface : g = G M p / r p 2

Homework: Find your gravitational force on the earths surface using universal G formula. (1lb = 0.45kg) Compare with the weight formula result. Compare with your gravitational force in orbit 300km above the earths surface. Find g for each planet and the moon. Find the escape velocity for each planet and the moon.

Rotational Speed (angular speed) The number of rotations/unit of time. RPM = rotations/min

Centripetal Force Centripetal force is a force that causes an object to travel in a circle.

How does mass impact Centripetal Force

Centrifugal Force Centrifugal means Center-fleeing and it is a force that seems to push you outward. Think playground Merry-go- Round

What it really is is inertia. Newtons First Law applies always.

Inertia, Centrifugal Force In a car.

Kids, Dont try this at home Experts state that you can swing a bucket of water over your head and it wont fall out because of centrifugal force (INERTIA). What they dont say is that when you stop swinging, it will drench you!

The breaking string revisited What kind of tension would be in that string?

In action

Rotational Mechanics Torque Rotational analog of Force; Produces rotation More leverage = More Torque

Torque changes the rotational motion of an object.

What is Torque?? Used when you use a hammer claw to remove a nail Used when you use a long- handled wrench to loosen a bolt The longer the handle, the greater the torque

Important facts to increase Torque The force must be applied perpendicular to the plane. The Longer the Lever, the greater the force.

Formula Torque = force (perpendicular) x Lever Arm

Look at the pictures on page 151. How does having the doorknob in the center of the door impact the torque?

See-Saw Torque When a large child and a small child play on the same see- saw, how do they balance the torques?

Triple Beam Balances Triple Beam Balances work the same way as the see-saw. You slide the weights on the arms to balance the torques. The same mass moved farther down the arm produces more torque.

Rotational motion and torque in an auto engine. http://science.howstuffworks.com/fpte4.htm

Torque Diagram

Torque measurement Torque = Force x lever arm

Torque & Center of Gravity Stand with your back and heels against the wall. Then try to lean forward to touch your toes. What happens to you??

You now have your center of gravity located somewhere other than over your feet, so you

See the sketches on page 154. If you kick a football at its center of gravity, what happens? If you kick a football above or below its center of gravity, what happens?

Rotational Inertia Just like in the inertia as learned before An object that is rotating about its axis will continue to rotate about its axis. Rotational inertia depends on the mass of the object and the distribution of mass relative to the axis of rotation. The more mass and the further it is on average from the axis, the higher the moment of inertia.

See P285 (P262 Hons)

Moment of inertia for rotating objects is analogous to mass for objects in linear motion. Which will roll down a hill first, a basketball or a bowling ball? A tire or a wheel/tire assembly? A solid golf ball or a hollow lead sphere? A tennis ball or a ping-pong ball?

Angular momentum: Just like momentum (P = m v) for objects moving in a straight line Angular momentum, L = I , where L is the angular momentum, I is the moment of inertia and is angular speed. Angular momentum is conserved if there is no net external torque.

Examples: Skater Diver Aerialist skier / snowboarder Planets in elliptical orbits. Tornado Hurricane http://youtu.be/druWqXZnoeU

Newtons second law for rotation Ch 9:4 hons. Before we had F = ma Can you think of what the rotational equivalent might be? Net external orque = I X Where I is the moment of inertia and is angular acceleration.

Rotation and energy, Ch 9:5 hons. Before we had work = F x d What do you think the rotational equivalent of work might be? Kinetic energy = I x 2 Work (Joules) = Net external Torque x Homework : P156: Q13, 15, 18. P 281:28, 29, 31 and P282 Q43, 44, 45, 46

Baseball and torque Why does a batter choke up on the bat? Page 155

Formulas for rotational inertia See page 157 of the text book.

Which will roll down the slope faster? See page 158. The hoop will roll faster that has the least inertia. Why?

Gymnastics and Inertia What are the three principal axes of rotation of the human body? (page 159) Each axis has a different rotational inertia.

Angular Momentum Angular momentum is a vector quantity And the momentum is conserved. A gyroscope swivels around, but the spin stays the same. See page 161

See page 162 How does angular momentum impact the balance of a bicycle rider?

Conservation of Angular Momentum Law of Conservation of Angular Momentum states: If no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant.

Read page 163. How does that apply to figure skating?

Why does a cat land on its feet (usually) when it falls? Page 163

Space and Angular Momentum Read the box on page 163. How does angular momentum relate to the shape and speed of rotation of a galaxy?

rotational motion chapter 7 rotational motion motion about an axis of rotation. a record turntable...

Documents