Chapter 8 Rotational Motion

1.CIRCULAR MOTION Which parts on a merry-go-round move fastest? Which have greater rotational speeds? Examples of rotational motion: Earth rotates and revolves

2.ROTATIONAL INERTIA Law of inertia for rotating systems An object rotating about an axis tends to remain rotating at the same rate about the same axis unless interfered with by some external influence. Examples: bullet, arrow, and earth Demo – Football and Spinning BasketballDemo – Football and Spinning Basketball Demo - Whirly Tube (Zinger)Demo - Whirly Tube (Zinger) Demo – Whirly ShooterDemo – Whirly Shooter Demo - Disc GunDemo - Disc Gun Demo - Rubber BandsDemo - Rubber Bands

Demo - Inertia BarsDemo - Inertia Bars Moment of inertia (rotational inertia) The sluggishness of an object to changes in its state of rotational motion Distribution of mass is the key. Example: Tightrope walker

Demo - Ring and Disk on InclineDemo - Ring and Disk on Incline Demo – MetronomeDemo – Metronome Walking pendulumsWalking pendulums (bending knees)

Lecture Table Demo – Falling Meter SticksDemo – Falling Meter Sticks

3.TORQUE Rotational analog of force A torque changes the rotational state of motion. Torque = force x lever arm length It is a vector. Units - N. m or lb. ft

See-Saw F D = F D D D

F D = F D 50 lb 150 lb 2 ft x

Line of action of the force F Torque = Fl l l Cheater Pipe l F F l

4.CENTER OF MASS AND CENTER OF GRAVITY Center of mass - average position of mass Earth.. Center of gravity - average position of weight Very large meteor

Path of center of mass of a rotating object will be a straight line if no external forces act on the object.

Demo – Hammer Toss

Locating the Center of Gravity Demo – Meter StickDemo – Meter Stick Demo - Map of TexasDemo - Map of Texas Demo - Balancing EagleDemo - Balancing Eagle Demo - Curious GeorgeDemo - Curious George Demo – Picking Up CandyDemo – Picking Up Candy Center can be outside of the object. Examples: high jump and pole vaulting

Stability Demo - Tower of PisaDemo - Tower of Pisa Demo - Touching ToesDemo - Touching Toes Demo - Standing on ToesDemo - Standing on Toes Demo - Object Rolling UphillDemo - Object Rolling Uphill Video – Dog Center of MassVideo – Dog Center of Mass 1/6 1/8 1/4 1/2 Demo - Boards Over the EdgeDemo - Boards Over the Edge

Equilibrium - Unstable If an object is displaced slightly from equilibrium and released and the object moves to a new position, then the object was in a state of unstable equilibrium. Example: Ball on inverted bowl

Equilibrium - Stable If an object is displaced slightly from equilibrium and released and the object returns to its old position, then the object was in a state of stable equilibrium. Example: Ball in bowl

Equilibrium - Neutral If an object is displaced slightly from equilibrium and released and the object remains where it is, then it was in a state of neutral equilibrium. Example: Ball on horizontal surface

Centripetal force - center seeking force Examples: tin can and string, sling, moon and earth, car on circular path, flying cat 5.CENTRIPETAL FORCE Demo - Coin on Clothes HangerDemo - Coin on Clothes Hanger Demo - String, Ball, and TubeDemo - String, Ball, and Tube Demo - Loop the LoopDemo - Loop the Loop

6.CENTRIFUGAL FORCE Centrifugal force - center fleeing force Often confused with centripetal Examples: sling and bug in can Demo - Walk the LineDemo - Walk the Line Centrifugal force is attributed to inertia.

7.CENTRIFUGAL FORCE IN A ROTATING REFERENCE FRAME A frame of reference can influence our view of nature. For example: we observe a centrifugal force in a rotating frame of reference, yet it is a fictitious (pseudo) force. Centrifugal force stands alone (there is no action-reaction pair) - it is a fictitious force.

Another pseudo force - CoriolisAnother pseudo force - Coriolis

8.SIMULATED GRAVITY To get a = g, the proper rotation rate and the proper radius must be determined. Gravity gradients Jogging in space

9.ANGULAR MOMENTUM For a point object the angular momentum is r m v J = mvr Units - kg. m 2 /s or sl. ft 2 /s It is a vector. Here the vector is pointing toward you.

How do you change the angular momentum of an object? An external torque is required. Newton's first law for rotating systems: An object or system of objects will maintain its state of angular momentum unless acted upon by an unbalanced external torque.

The larger J is, the larger the torque must be to change it. Demo - Bicycle WheelDemo - Bicycle Wheel Demo - GyroscopeDemo - Gyroscope

10.CONSERVATION OF ANGULAR MOMENTUM If there are no external torques acting on a rotating system then angular momentum is conserved. This means the final angular momentum is equal to the initial angular momentum.

Examples: ice skater spin, diving, tides and moon Demo - "Ice Skater“Demo - "Ice Skater“ Movie – Ice SkaterMovie – Ice Skater Movie – SFA CheerleadersMovie – SFA Cheerleaders Demo - Bicycle Wheel and Rotating PlatformDemo - Bicycle Wheel and Rotating Platform Movie - J in Sky LabMovie - J in Sky Lab Movie - More J in Sky LabMovie - More J in Sky Lab

Chapter 8 Review Questions Chapter 8 Review Questions

In walking, people normally bend their knees. Why? (a) it is easier to swing their legs because bending lowers the rotational inertia of their legs (b) it is easier to swing their legs because bending increases the rotational inertia of their legs

Which is harder to stop? A rotating rod with its mass predominantly at the (a) middle of the rod (b) ends of the rod (c) neither of the above

A ball is at rest on a horizontal table. It is in a state of equilibrium. (a) neutral (b) stable (c) unstable (d) both (a) and (b) (e) both (a) and (c)

Which of the following forces is a pseudo force? (a) tension in a rope (b) force of gravity (c) centripetal (d) friction (e) centrifugal

What is the angular momentum of a 6 kg mass traveling with a speed of 6 m/s in a circle of radius of 12 m? (a) 432 kg·m 2 /s (b) 12 kg·m 2 /s (c) 24 kg·m 2 /s (d) 144 kg·m 2 /s (e) 36 kg·m 2 /s