Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

Lecture 2- RotationChapter 11

Prof. Noronha-HostlerPHY-124H HONOROS ANALYTICAL PHYSICS IB

Phys- 124HJan. 26th, 2018

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Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

WebAssign

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Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

Center of Mass of Wheel

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Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

Types of rolling motion

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11.2.3. A circular hoop rolls without slipping on a flat horizontal surface. Which one of the following is necessarily true?

a) All points on the rim of the hoop have the same speed.

b) All points on the rim of the hoop have the same velocity.

c) Every point on the rim of the wheel has a different velocity.

d) All points on the rim of the hoop have acceleration vectors that are tangent to the hoop.

e) All points on the rim of the hoop have acceleration vectors that point toward the center of the hoop.

11.2.3. A circular hoop rolls without slipping on a flat horizontal surface. Which one of the following is necessarily true?

a) All points on the rim of the hoop have the same speed.

b) All points on the rim of the hoop have the same velocity.

c) Every point on the rim of the wheel has a different velocity.

d) All points on the rim of the hoop have acceleration vectors that are tangent to the hoop.

e) All points on the rim of the hoop have acceleration vectors that point toward the center of the hoop.

11.2.4. A bicycle wheel of radius 0.70 m is turning at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. What is the linear speed of the wheel?

a) 1.4 m/s

b) 28 m/s

c) 0.11 m/s

d) 4.4 m/s

e) 9.1 m/s

11.2.4. A bicycle wheel of radius 0.70 m is turning at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. What is the linear speed of the wheel?

a) 1.4 m/s

b) 28 m/s

c) 0.11 m/s

d) 4.4 m/s

e) 9.1 m/s

11.3.2. A hollow cylinder is rotating about an axis that passes through the center of both ends. The radius of the cylinder is r. At what angular speed must the this cylinder rotate to have the same total kinetic energy that it would have if it were moving horizontally with a speed v without rotation?

a)

b)

c)

d)

e)

2

2

v

r

2v

r

v

r

2

v

r

2

2

v

r

11.3.2. A hollow cylinder is rotating about an axis that passes through the center of both ends. The radius of the cylinder is r. At what angular speed must the this cylinder rotate to have the same total kinetic energy that it would have if it were moving horizontally with a speed v without rotation?

a)

b)

c)

d)

e)

2

2

v

r

2v

r

v

r

2

v

r

2

2

v

r

Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

Inclined Plane

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11.4.1. A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M slides down an identical inclined plane. Complete the following statement: If both objects are released at the same time,

a) the cylinder will reach the bottom first.

b) the block will reach the bottom first.

c) the block will reach the bottom with the greater kinetic energy.

d) the cylinder will reach the bottom with the greater kinetic energy.

e) both the block and the cylinder will reach the bottom at the same time.

11.4.1. A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M slides down an identical inclined plane. Complete the following statement: If both objects are released at the same time,

a) the cylinder will reach the bottom first.

b) the block will reach the bottom first.

c) the block will reach the bottom with the greater kinetic energy.

d) the cylinder will reach the bottom with the greater kinetic energy.

e) both the block and the cylinder will reach the bottom at the same time.

Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

Torque direction

Use right hand rule. Torque pointing in positive z direction.

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11.7.2. What is the direction of the Earth’s orbital angular momentum as it spins about its axis?

a) north

b) south

c) east

d) west

e) radially inward

11.7.2. What is the direction of the Earth’s orbital angular momentum as it spins about its axis?

a) north

b) south

c) east

d) west

e) radially inward

Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

Linear to Angular

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11.11.1. A star is rotating about an axis that passes through its center. When the star “dies,” the balance between the inward pressure due to the force of gravity and the outward pressure from nuclear processes is no longer present and the star collapses inward and its radius decreases with time. Which one of the following choices best describes what happens as the star collapses?

a) The angular velocity of the star remains constant.

b) The angular momentum of the star remains constant.

c) The angular velocity of the star decreases.

d) The angular momentum of the star decreases.

e) Both angular momentum and angular velocity increase.

11.11.1. A star is rotating about an axis that passes through its center. When the star “dies,” the balance between the inward pressure due to the force of gravity and the outward pressure from nuclear processes is no longer present and the star collapses inward and its radius decreases with time. Which one of the following choices best describes what happens as the star collapses?

a) The angular velocity of the star remains constant.

b) The angular momentum of the star remains constant.

c) The angular velocity of the star decreases.

d) The angular momentum of the star decreases.

e) Both angular momentum and angular velocity increase.

11.12.1. The precession of a gyroscope is an example of which of the following principles?

a) conservation of rotational energy

b) conservation of angular momentum

c) conservation of linear momentum

d) conservation of total mechanical energy

e) conservation of torque

11.12.1. The precession of a gyroscope is an example of which of the following principles?

a) conservation of rotational energy

b) conservation of angular momentum

c) conservation of linear momentum

d) conservation of total mechanical energy

e) conservation of torque

Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

Gyroscope

Not spinning wheel Spinning wheel

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Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo

Yo-Yo

Treat as a wheel rolling on 90◦ plane

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