4-Sep-15 Physics 1 (Garcia) SJSU Chapter 8 Rotational Motion

Rotational Motion In physics we distinguish two types of motion for objects: Translational Motion (change of location) Rotational Motion (change of orientation) We’ve mostly discussed translational motion; today we consider rotation.

4-Sep-15 Physics 1 (Garcia) SJSU Circles Circumference is distance around the perimeter of the circle. Small circle is half the radius so half the diameter and half the circumference. Axis Radius Diameter Axis Radius Diameter

4-Sep-15 Physics 1 (Garcia) SJSU Circular Motion Rotational Speed: Revolutions per second Tangential Speed: Total distance per second Same Rotational Speed Different Tangential Speeds

4-Sep-15 Physics 1 (Garcia) SJSU Check Yourself A pair of wheels are connected by a chain. Which wheel has higher rotational speed? By how much? Faster tangential speed on rim? 1 2

4-Sep-15 Physics 1 (Garcia) SJSU Bicycles FAST SLOW Notice how gears work on a modern bicycle

4-Sep-15 Physics 1 (Garcia) SJSU Simple & Complex Objects Motion of simple objects: Position Motion of complex objects: Position & Rotation SIMPLE COMPLEX Axis of Rotation

4-Sep-15 Physics 1 (Garcia) SJSU Mass is a measure of inertia for linear motion. Rotational inertia is similar concept for rotation. Inertia M m Gold brick Normal brick Difficult to move Easy to move x x Wood Bat Plastic Pee-wee Bat Difficult to Rotate Easy to Rotate

4-Sep-15 Physics 1 (Garcia) SJSU Rotational Inertia Rotational inertia depends on Total mass of the object Distribution of the mass Farther the mass is from the axis of rotation, the larger the rotational inertia. Rotational inertia goes as (mass) x (distance) 2

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Inertia Sticks Two metal pipes of the same mass Rotate Easy to Rotate Hard to Rotate

Check Yourself Which dancer has greater rotational inertia? Axis of Rotation A B

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Hammer Balance When is the hammer easier to balance on your finger? B A

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Drop the Stick Two meter sticks stand upright against a wall; one has a hunk of clay on the end. Which stick will swing down and hit the floor first? Why?

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Long Legs Long legs have greater rotational inertia than short legs so long legged animals have a slow walking stride.

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Ramp Racing The two disks and rods have the same mass but one has connecting rods near the center while the other has rods near the rim. When rolled down a ramp, which wins the race? Winner

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Hoop & Disk Racing Roll a hoop and a disk down a ramp; which wins the race?

4-Sep-15 Physics 1 (Garcia) SJSU When a force causes a rotation, we identify this as a torque. Torque depends on Magnitude of Force Direction of Force Lever Arm (Torque) = (Force) x (Lever Arm) Torque

4-Sep-15 Physics 1 (Garcia) SJSU Lever Arm Lever arm is perpendicular distance from axis of rotation to the direction of the force.

4-Sep-15 Physics 1 (Garcia) SJSU Check Yourself Identify the lever arm for each wrench. Force Which wrench design gives the most torque?

Torque for a Pirouette The farther the distance between the feet, the greater the lever arm so the greater the torque for creating the rotation. Push on Floor Reaction Force Lever Arm Feet apart Feet together

4-Sep-15 Physics 1 (Garcia) SJSU Check Yourself In which case are you exerting more torque? A B Lever Arm almost zero

4-Sep-15 Physics 1 (Garcia) SJSU Balance of Torques Torques clockwise and counter-clockwise balance in both cases since (250 N) x (3 m) = (500 N) x (1.5 m) Her lever arm is 3 meters

4-Sep-15 Physics 1 (Garcia) SJSU Center of Mass/Gravity Average position of all the mass in an object is called the center of mass (CM). Average position of the weight distribution is called the center of gravity (CG). When gravity is constant these two locations are the same.

4-Sep-15 Physics 1 (Garcia) SJSU Locating Center of Gravity Balance an object to find center of gravity Center of Gravity

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Balance the Can If a small amount of water is added to an empty soda can then the can may be balanced on its bottom edge. x CG PEPSI

4-Sep-15 Physics 1 (Garcia) SJSU Stability Object is stable if CG is above the base. CG Weight BASE Axis BASE STABLE UNSTABLE

4-Sep-15 Physics 1 (Garcia) SJSU Check Yourself Three trucks are parked on a slope. Which truck(s) tip over? CG BASE

Balance & Ballet Center of Gravity located above the dancer’s toe The force of gravity and the support force of the floor can balance only when a dancer’s center of gravity is located above the base of support.

Balance Beam You tend to hold your arms out when on a balance beam for two reasons: Increase your rotational inertia so as to slow your rate of tipping over. Allow rapid changes of your center of gravity, to regain balance

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Balanced Bird Where is the bird’s center of gravity?

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Mystery Wheel Wheel doesn’t roll down hill. How is that possible?

4-Sep-15 Physics 1 (Garcia) SJSU Centripetal Force Centripetal means “towards the center.” Whenever an object moves along a circular path there must be a force on that object in the direction of the center of the circle. In such a case, the force is said to be centripetal.

4-Sep-15 Physics 1 (Garcia) SJSU Check Yourself A BC D Object rotates in a circle on the end of a string. Is there a force on the object? What causes the force? In what direction is the force?

4-Sep-15 Physics 1 (Garcia) SJSU Centripetal Force Examples Friction force (tires) is centripetal. Tension force (string) is centripetal. Gravity force (on satellite due to Earth) is centripetal

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Around the Ring The support force exerted by the wall of the ring is centripetal. Ball moves in a straight line once the force is removed (ball leaves the ring). Support Force

4-Sep-15 Physics 1 (Garcia) SJSU Magnitude of Centripetal Force Magnitude of centripetal force is large when Speed is large Radius is small Mass is large

4-Sep-15 Physics 1 (Garcia) SJSU Hurricanes Rita, 9/22/05 L H H – High Pressure L – Low Pressure F – Centripetal Force due to pressure difference F Hurricane’s strength (wind speed) depends on how low the pressure gets in the center.

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Loop-the-Loop If the speed of the ball is large then the support force of the track is required to keep it moving in a circle. Velocity Release This is also a good demo for conservation of kinetic + potential energy.

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Loop-the-Loop Ball could even circle a loop with a gap, if the speed was just right so gravity was just the right amount of centripetal force. Velocity Release GAP

4-Sep-15 Physics 1 (Garcia) SJSU Centrifugal Force What we see What the insect feels Insect inside a can rotating in a circle When a centripetal force acts on an object, it appears to the object that there is an outward force. Call this apparent force the centrifugal force.

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Bucket Overhead Can put a bucket full of water over my head without getting wet by rotating it fast enough. Forces exerted on the water by gravity plus support force of the bucket are centripetal. Apparent centrifugal force presses the water into the bucket. Centripetal Force Centrifugal Force

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Bucket Overhead Throw a bowling ball or ball of water overhead. As long as the speed is fast enough it will sail overhead in a curved path. Gravity by itself supplies the centripetal force. Gravity

4-Sep-15 Physics 1 (Garcia) SJSU Simulated Gravity Centrifugal force could be used to simulate gravity in a space station. With the right rate of rotation a person on the outer rim would feel as if they stood on the surface of Earth. Scientifically accurate in the movie 2001: A Space Odyssey (1968) Rotation

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Spin Out Everyday examples of “enhanced” gravity: Salad spinner. Spin cycle in washer. Centrifuge.

4-Sep-15 Physics 1 (Garcia) SJSU Angular Momentum There are two types of momentum (Linear Momentum) = (Mass) x (Velocity) and (Angular Momentum) = (Rotational Inertia) x (Rotational Velocity) Principle of conservation for both types.

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Skater’s Spin By moving their outstretched arms and legs inward an ice skater can decrease their body’s rotational inertia. By conservation of angular momentum, they increase their angular velocity (spin faster)

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Skater’s Spin Slow Rotation FAST Rotation LARGE Inertia Small Inertia Angular momentum is constant since (Rotational Inertia) x (Angular Velocity) remains constant.

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Flip the Wheel Counter- Clockwise Rotation Counter- Clockwise Rotation Clockwise Rotation Similar to collisions

4-Sep-15 Physics 1 (Garcia) SJSU Demo: Spin Up Zero Rotation Clockwise Rotation Counter- Clockwise Rotation Similar to recoil

4-Sep-15 Physics 1 (Garcia) SJSU Blades Body Helicopter’s Tail When a helicopter’s blades start turning in one direction, by conservation of angular momentum the body would spin in the opposite direction. To compensate, the small rotor in the tail exerts a torque to balance.

Demo: Mid-Air Twist Stand up and clear space around you. When I say “Jump!”, jump. In mid-air I’ll point left or right and I want you to try to turn so you land facing that direction. Jump! Turn Land How can you rotate in mid-air without pushing off of anything?

Demo: Mid-Air Twist Jump! Turn Land As you turn your legs 90 degrees, your arms and torso rotate in the opposite direction. Sticking your arms out as you turn helps by increasing the rotational inertia of your upper body. A large rotation of your legs is exactly cancelled by a small rotation of your outspread arms and torso. Your rotation stops as soon as you stop rotating your upper body but by that time you’ve landed with your feet turned to the side. Once on the ground you can push off on the ground to restore your arms and torso to a normal stance.