PHY 131 H 1 S Class 20 Today
![PHY 131 H 1 S - Class 20 Today: • Gravitational Torque • Rotational PHY 131 H 1 S - Class 20 Today: • Gravitational Torque • Rotational](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-1.jpg)
![Pre-class reading quiz on Chapter 12 Pre-class reading quiz on Chapter 12](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-2.jpg)
![Last day I asked at the end of class: • Why did that wooden Last day I asked at the end of class: • Why did that wooden](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-3.jpg)
![Gravitational Torque • When calculating the torque due to gravity, you may treat the Gravitational Torque • When calculating the torque due to gravity, you may treat the](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-4.jpg)
![Example 12. 10 • A 4. 00 m long, 500 kg steel beam is Example 12. 10 • A 4. 00 m long, 500 kg steel beam is](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-5.jpg)
![“Rolling Without Slipping” When a round object rolls without slipping, the distance the axis, “Rolling Without Slipping” When a round object rolls without slipping, the distance the axis,](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-6.jpg)
![Examples: • What is the acceleration of a slipping object down a ramp inclined Examples: • What is the acceleration of a slipping object down a ramp inclined](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-7.jpg)
![Linear / Rotational Analogy Linear • , , • Force: • Mass: m • Linear / Rotational Analogy Linear • , , • Force: • Mass: m •](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-8.jpg)
![Rotational Energy A rotating rigid body has kinetic energy because all atoms in the Rotational Energy A rotating rigid body has kinetic energy because all atoms in the](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-9.jpg)
![Summary of some Different Types of Energy: • Kinetic Energy due to linear motion Summary of some Different Types of Energy: • Kinetic Energy due to linear motion](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-10.jpg)
![Updated Conservation of Energy… Updated Conservation of Energy…](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-11.jpg)
![Compare and Contrast Soup Cans • About same mass • About same radius and Compare and Contrast Soup Cans • About same mass • About same radius and](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-12.jpg)
![Soup Race • Two soup cans begin at the top of an incline, are Soup Race • Two soup cans begin at the top of an incline, are](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-13.jpg)
![Equilibrium When Rotation is Possible • The condition for a rigid body to be Equilibrium When Rotation is Possible • The condition for a rigid body to be](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-14.jpg)
![Static Equilibrium Problems • In equilibrium, an object has no net force and no Static Equilibrium Problems • In equilibrium, an object has no net force and no](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-15.jpg)
![](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-16.jpg)
![A student holds a meter stick straight out with one or more masses dangling A student holds a meter stick straight out with one or more masses dangling](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-17.jpg)
![The Angular Velocity Vector • The magnitude of the angular velocity vector is ω. The Angular Velocity Vector • The magnitude of the angular velocity vector is ω.](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-18.jpg)
![Linear / Rotational Analogy Linear • , , • Force: • Mass: m • Linear / Rotational Analogy Linear • , , • Force: • Mass: m •](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-19.jpg)
![• A bicycle is traveling toward the right. • A bicycle is traveling toward the right.](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-20.jpg)
![• If there is no net external force on a system, then its • If there is no net external force on a system, then its](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-21.jpg)
![I is high I is low is constant when there are no external torques. I is high I is low is constant when there are no external torques.](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-22.jpg)
![Two buckets spin around in a horizontal circle on frictionless bearings. Suddenly, it starts Two buckets spin around in a horizontal circle on frictionless bearings. Suddenly, it starts](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-23.jpg)
![Before Class 21 on Monday • There is a Mastering. Physics problem set due Before Class 21 on Monday • There is a Mastering. Physics problem set due](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-24.jpg)
- Slides: 24
![PHY 131 H 1 S Class 20 Today Gravitational Torque Rotational PHY 131 H 1 S - Class 20 Today: • Gravitational Torque • Rotational](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-1.jpg)
PHY 131 H 1 S - Class 20 Today: • Gravitational Torque • Rotational Kinetic Energy • Rolling without Slipping • Equilibrium with Rotation • Rotation Vectors • Angular Momentum
![Preclass reading quiz on Chapter 12 Pre-class reading quiz on Chapter 12](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-2.jpg)
Pre-class reading quiz on Chapter 12
![Last day I asked at the end of class Why did that wooden Last day I asked at the end of class: • Why did that wooden](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-3.jpg)
Last day I asked at the end of class: • Why did that wooden disk roll faster down the hill than the metal hoop? • ANSWER:
![Gravitational Torque When calculating the torque due to gravity you may treat the Gravitational Torque • When calculating the torque due to gravity, you may treat the](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-4.jpg)
Gravitational Torque • When calculating the torque due to gravity, you may treat the object as if
![Example 12 10 A 4 00 m long 500 kg steel beam is Example 12. 10 • A 4. 00 m long, 500 kg steel beam is](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-5.jpg)
Example 12. 10 • A 4. 00 m long, 500 kg steel beam is supported 1. 20 m from the right end. What is the gravitational torque about the support?
![Rolling Without Slipping When a round object rolls without slipping the distance the axis “Rolling Without Slipping” When a round object rolls without slipping, the distance the axis,](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-6.jpg)
“Rolling Without Slipping” When a round object rolls without slipping, the distance the axis, or centre of mass, travels is equal to the change in angular position times the radius of the object. The speed of the centre of mass is The acceleration of the centre of mass is
![Examples What is the acceleration of a slipping object down a ramp inclined Examples: • What is the acceleration of a slipping object down a ramp inclined](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-7.jpg)
Examples: • What is the acceleration of a slipping object down a ramp inclined at angle θ? [assume no friction] • What is the acceleration of a solid disk rolling down a ramp inclined at angle θ? [assume rolling without slipping] • What is the acceleration of a hoop rolling down a ramp inclined at angle θ? [assume rolling without slipping]
![Linear Rotational Analogy Linear Force Mass m Linear / Rotational Analogy Linear • , , • Force: • Mass: m •](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-8.jpg)
Linear / Rotational Analogy Linear • , , • Force: • Mass: m • Newton’s 2 nd law: • Kinetic energy: Rotational Analogy • θ, ω, α • Torque: τ • Moment of Inertia: I
![Rotational Energy A rotating rigid body has kinetic energy because all atoms in the Rotational Energy A rotating rigid body has kinetic energy because all atoms in the](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-9.jpg)
Rotational Energy A rotating rigid body has kinetic energy because all atoms in the object are in motion. The kinetic energy due to rotation is called rotational kinetic energy. Example: A 0. 50 kg basketball rolls along the ground at 1. 0 m/s. What is its total kinetic energy? [linear plus rotational]
![Summary of some Different Types of Energy Kinetic Energy due to linear motion Summary of some Different Types of Energy: • Kinetic Energy due to linear motion](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-10.jpg)
Summary of some Different Types of Energy: • Kinetic Energy due to linear motion of centre of mass: • Gravitational Potential Energy • Spring Potential Energy: • Rotational Kinetic Energy: • Thermal Energy (often created by friction) – An object can possess any or all of the above. – One way of transferring energy to or out of an object is work: • Work done by a constant force:
![Updated Conservation of Energy Updated Conservation of Energy…](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-11.jpg)
Updated Conservation of Energy…
![Compare and Contrast Soup Cans About same mass About same radius and Compare and Contrast Soup Cans • About same mass • About same radius and](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-12.jpg)
Compare and Contrast Soup Cans • About same mass • About same radius and shape • Thick paste, so when this can is rolling, the contents rotate along with the can as one solid object, like a solid cylinder • Low viscosity liquid, so the can itself rolls while the liquid may just “slide” along.
![Soup Race Two soup cans begin at the top of an incline are Soup Race • Two soup cans begin at the top of an incline, are](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-13.jpg)
Soup Race • Two soup cans begin at the top of an incline, are released from rest, and allowed to roll without slipping down to the bottom. Which will win? Predict: A. Cream of Mushroom will win B. Chicken Broth will win C. Both will reach the bottom at about the same time.
![Equilibrium When Rotation is Possible The condition for a rigid body to be Equilibrium When Rotation is Possible • The condition for a rigid body to be](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-14.jpg)
Equilibrium When Rotation is Possible • The condition for a rigid body to be in static equilibrium is that there is no net force and no net torque. • An important branch of engineering called statics analyzes buildings, dams, bridges, and other structures in total static equilibrium. • No matter which pivot point you choose, an object that is not rotating about that point. • For a rigid body in total equilibrium, there is no net torque about any point.
![Static Equilibrium Problems In equilibrium an object has no net force and no Static Equilibrium Problems • In equilibrium, an object has no net force and no](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-15.jpg)
Static Equilibrium Problems • In equilibrium, an object has no net force and no net torque. • Draw an extended free-body diagram that shows where each force acts on the object. • Set up x and y axes, and choose a rotation axis. All of these choices should be done to simplify your calculations. • Each force has an x and y component and a torque. Sum all of these up. • Three equations which you can use are:
![](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-16.jpg)
![A student holds a meter stick straight out with one or more masses dangling A student holds a meter stick straight out with one or more masses dangling](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-17.jpg)
A student holds a meter stick straight out with one or more masses dangling from it. Rank in order, from most difficult to least difficult, how hard it will be for the student to keep the meter stick from rotating.
![The Angular Velocity Vector The magnitude of the angular velocity vector is ω The Angular Velocity Vector • The magnitude of the angular velocity vector is ω.](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-18.jpg)
The Angular Velocity Vector • The magnitude of the angular velocity vector is ω. • The angular velocity vector points along the axis of rotation in the direction given by the right-hand rule as illustrated above.
![Linear Rotational Analogy Linear Force Mass m Linear / Rotational Analogy Linear • , , • Force: • Mass: m •](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-19.jpg)
Linear / Rotational Analogy Linear • , , • Force: • Mass: m • Newton’s 2 nd law: • Kinetic energy: • Momentum: Rotational Analogy • θ, ω, α • Torque: τ • Moment of Inertia: I
![A bicycle is traveling toward the right • A bicycle is traveling toward the right.](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-20.jpg)
• A bicycle is traveling toward the right.
![If there is no net external force on a system then its • If there is no net external force on a system, then its](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-21.jpg)
• If there is no net external force on a system, then its momentum is a constant. • If there is no work or heat being exchanged with a system and its surroundings, then its energy is constant. • If there is no net external torque on a system, then its angular momentum is a constant.
![I is high I is low is constant when there are no external torques I is high I is low is constant when there are no external torques.](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-22.jpg)
I is high I is low is constant when there are no external torques.
![Two buckets spin around in a horizontal circle on frictionless bearings Suddenly it starts Two buckets spin around in a horizontal circle on frictionless bearings. Suddenly, it starts](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-23.jpg)
Two buckets spin around in a horizontal circle on frictionless bearings. Suddenly, it starts to rain. As a result,
![Before Class 21 on Monday There is a Mastering Physics problem set due Before Class 21 on Monday • There is a Mastering. Physics problem set due](https://slidetodoc.com/presentation_image_h2/5188942fc938561d6d4f3fd694659b6f/image-24.jpg)
Before Class 21 on Monday • There is a Mastering. Physics problem set due tonight! Please submit this before 11: 59 pm if you have not already done so. • Please read Knight Chapter 14, sections 14. 1 through 14. 3. • Something to think about: A block is oscillating on a spring with a period of 2 seconds. • What is the period if the mass is doubled? • What is the period if the spring constant is doubled?
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