Linear Momentum & Rotational Motion Flashcards

Linear Momentum & Rotational Motion Flashcards
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The moon (7.35 * 1022 kg) revolves around Earth with a radius of 3.8 * 105 km at a speed of 1 km/s. What is the force of gravity that Earth exerts on the moon?

Fg = mv2 / r = 7.35 * 1022 kg * (1000 m/s)2 / 3.8 * 108 m = 1.9 * 1020 N

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Name the rotational equivalents of acceleration, force, momentum, velocity, and mass.

Acceleration = angular acceleration, force = torque, momentum = angular momentum, velocity = angular velocity, mass = moment of inertia

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Torque

An off-center force exerted on an object, causing it to spin

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A 5 kg mass traveling east at 10 m/s collides inelastically with a 3 kg mass traveling west at 4 m/s. Determine the velocity of the combined masses after the collision.

m1 * v1 + m2 * v2 = (m1 + m2) * vf

(5 kg)(10 m/s) + (3 kg)(-4 m/s) = (5 kg + 3 kg) * vf

vf = 4.75 m/s east

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A 3,000 kg truck is traveling at 20 m/s. If the driver slams on the brakes and it generates force of 8,000 N on the driver, determine the amount of time it took to stop.

Force * time = change in momentum

Change in momentum = 3000 kg * 0 m/s - 3000 kg * 20 m/s = -60,000 kg m/s

Time = 60,000 kg m/s / 8,000 N = 7.5 seconds

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A 500 kg motorcycle moving 10 m/s has an elastic collision with a 1000 kg car at 12 m/s in the same direction. Determine the velocity of the motorcycle if the car is now moving at 14 m/s.

m1 * vi1 + m2 * vi2 = m1 * vf1 + m2 * vf2

(500 kg)(10 m/s) + (1000 kg)(12 m/s) = (500 kg)(vf1) + (1000 kg)(14 m/s)

vf1 = 6 m/s

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Inelastic Collision

An event in which two objects collide, resulting in permanent deformation or being stuck together and loss of heat

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Elastic Collision

An event in which two objects collide, resulting in no permanent deformation or loss of heat

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Isolated System

An environment containing two or more objects in which the total amount of energy does not change

No external net forces

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Momentum

A conserved quantity that measures a mass in motion

Can only be changed by a force external to a system

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Find the momentum of 3,000 kg object moving at 10 m/s.

Momentum = mass * velocity = 3,000 kg * 10 m/s = 30,000 kg m/s

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22 cards in set

Flashcard Content Overview

In these flashcards, you will first review momentum. This includes what momentum is, how to calculate it, two different types of collisions, and the conservation of momentum. Second, you will review the relationship between translational and rotational motion and see how many equations you already know for objects moving in a linear direction can be slightly changed to solve problems involving objects moving in a circle.

Front
Back
Find the momentum of 3,000 kg object moving at 10 m/s.

Momentum = mass * velocity = 3,000 kg * 10 m/s = 30,000 kg m/s

Momentum

A conserved quantity that measures a mass in motion

Can only be changed by a force external to a system

Isolated System

An environment containing two or more objects in which the total amount of energy does not change

No external net forces

Elastic Collision

An event in which two objects collide, resulting in no permanent deformation or loss of heat

Inelastic Collision

An event in which two objects collide, resulting in permanent deformation or being stuck together and loss of heat

A 500 kg motorcycle moving 10 m/s has an elastic collision with a 1000 kg car at 12 m/s in the same direction. Determine the velocity of the motorcycle if the car is now moving at 14 m/s.

m1 * vi1 + m2 * vi2 = m1 * vf1 + m2 * vf2

(500 kg)(10 m/s) + (1000 kg)(12 m/s) = (500 kg)(vf1) + (1000 kg)(14 m/s)

vf1 = 6 m/s

A 3,000 kg truck is traveling at 20 m/s. If the driver slams on the brakes and it generates force of 8,000 N on the driver, determine the amount of time it took to stop.

Force * time = change in momentum

Change in momentum = 3000 kg * 0 m/s - 3000 kg * 20 m/s = -60,000 kg m/s

Time = 60,000 kg m/s / 8,000 N = 7.5 seconds

A 5 kg mass traveling east at 10 m/s collides inelastically with a 3 kg mass traveling west at 4 m/s. Determine the velocity of the combined masses after the collision.

m1 * v1 + m2 * v2 = (m1 + m2) * vf

(5 kg)(10 m/s) + (3 kg)(-4 m/s) = (5 kg + 3 kg) * vf

vf = 4.75 m/s east

Torque

An off-center force exerted on an object, causing it to spin

Name the rotational equivalents of acceleration, force, momentum, velocity, and mass.

Acceleration = angular acceleration, force = torque, momentum = angular momentum, velocity = angular velocity, mass = moment of inertia

The moon (7.35 * 1022 kg) revolves around Earth with a radius of 3.8 * 105 km at a speed of 1 km/s. What is the force of gravity that Earth exerts on the moon?

Fg = mv2 / r = 7.35 * 1022 kg * (1000 m/s)2 / 3.8 * 108 m = 1.9 * 1020 N

Stable Equilibrium

A state that an object is in when, if slightly disturbed, it returns to its original position

Tilting raises the center of gravity

Unstable Equilibrium

A state that an object is in when, if slightly disturbed, it tips over

Tilting lowers the center of gravity

Determine the tension a string feels if it is 0.5 m long and used to spin a 1.0 kg object in a circle at a speed of 5 m/s.

Fc = mv2 / r = 1.0 kg * (5 m/s)2 / 0.5 m = 50 N

Centripetal Acceleration

Occurs because when an object is experiencing circular motion, the direction is always changing despite traveling at the same speed

ac = v2 / r

Angular Velocity

A measure of how fast an object is rotating, with radians per second as the unit

Equation: angular velocity = change in angle / time

Angular Acceleration

A measure of the rate of change in angular velocity, with radians per second squared as the unit

Occurs when an object's rotational speed is changing (different than centripetal acceleration)

A cyclist pedaling at 60 rotations per minute (6.3 rad/s) speeds up to 90 rotations per minute (9.4 rad/s). If it takes the cyclist 5 seconds to speed up, determine how far the wheel turned.

θ = (ωf + ωi) * t / 2 = (9.4 rad/s + 6.3 rad/s) * 5 s / 2 = 39.2 radians

A 10 kg mass is hanging from a 5 m board that is attached to the wall with a bracket. Determine the amount of torque experienced by the bracket.

Torque = Fr = 10 kg * 9.8 m/s2 * 5 m = 490 Nm

Determine the rotational kinetic energy of a merry-go-round with a moment of inertia of 25 kg m2 and an angular velocity of 10 rotations every 2 minutes.

10 rotations/2 minutes = 5 rotations/min = 0.52 rad/s

Kinetic energy = 1/2 * moment of inertia * angular velocity2 = 1/2 * 25 kg m2 * (0.52 rad/s)2 = 3.38 J

A plumber applies 200 N of force on a 15 cm long wrench, making a half turn on a pipe. Determine the work done by the plumber.

1/2 turn = 3.14 radians

Work = torque * rotation = 200 N * 0.15 m * 3.14 radians = 94.2 J

A plumber applies 200 N of force on a 15 cm long wrench, making a half turn on a pipe. Determine the angular velocity of the wrench if the plumber exerted 188.4 watts of power.

1/2 turn = 3.14 radians

Power = work/time But work = [torque x θ (change in angle)]

Power = [torque x θ] / time.

And, θ / time = angular velocity

So, Power = torque x angular velocity

188.4 Watts = [200 N x 0.15 m x 3.14 radians] x angular velocity

2 radians /s = angular velocity

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