Physics Test 3

Position x is equilivant to ________

θ angular position

Velocity v is equivalent to _________

w angular velocity

Acceleration a is equivalent to __________

a angular acceleration

Force f is equivalent to __________

T torque (rotational force)

What is θ?

Angle measured from reference line

SI units: radian (rad) which is dimensionless!

θ > 0

Counterclockwise rotation

θ < 0

Clockwise rotation

Other units:

1 rev = 360 degrees = 2π rad

What’s a radian?

The angle for which the arc length on a circle is equal to the radius

Arc length:

s = rθ

Angular displacement:

Δθ

Average angular velocity (w) SI units

rad/s = s^-1

Average angular acceleration (a) SI units?

rad/s² = s^-2

If angular acceleration and angular velocity are in the same direction, angular speed ________.

increases

What does tangential describe?

changing speed

What does centripetal describe?

changing direction

Degrees to radians:

Multiply by 2π/ 360

Degrees to revolutions:

Divide by 360

Radians to degrees:

Multiple by 360/ 2π

Radians to revolutions

Divide by 2π

Revolutions to degrees:

Multiply by 360

Revolutions to radians

Multiply by 2π

We can view rolling without slipping as a combination of purely ________ and purely ________.

rotational motion; translational motion

When applying a force to make an object rotate, it’s easier if you apply the force __________ from the axis of rotation.

farther away

Two bugs sits on a turntable, bug 1 sits on the outer edge of a turntable, and bug 2 sits halfway between bug 1 and the axis of rotation. The turntable makes one complete revolution every second. The second bug’s linear speed is ….

A) … half the linear speed of bug 1

B) … the same as the linear speed of bug 1

C) … twice the linear speed of bug 1

D) Impossible to determine

A) … half the linear speed of bug 1

A wheel of radius 0.50 m is rotating with an angular speed of 4.0 rad/s. What is the tangential (linear) speed of a point on the edge of the wheel?

2.0 m/s

In linear motion, a constant acceleration changes an object’s velocity according to vf = vi + aㆍt. Which equation describes the equivalent relationship for rotational motion with constant angular acceleration?

A) θf = θi + ωi t

B) ωf = ωi + α t

C) ωf = ωi + τ t

D) α = ωi t + ½ ωf t^2

B) ωf = ωi + α t

When applying a force to make an object rotate, it is easier if you apply the force _______ away from the axis of rotation.

farther

For rotational motion, the _______ of the force matters as well as the magnitude.

location

Only the _______ component contributes to the torque.

tangential

If a torque tends to cause a counterclockwise rotation, it is _________.

positive

If a torque tends to cause a clockwise rotation, it is _________.

negative

A student pushes on a door to open it. The door rotates about its hinges. Which statement about torque is correct?

A) Torque is the rotational equivalent of velocity.

B) Torque depends only on the magnitude of the applied force.

C) Torque is the rotational equivalent of force and can cause angular acceleration.

D) A force always produces the same torque, regardless of where it is applied.

C) Torque is the rotational equivalent of force and can cause angular acceleration.

In rotational motion, the moment of inertia plays a role analogous to which quantity in linear motion?

A) Force

B) Mass

C) Velocity

D) Acceleration

B) Mass

A disk and a hoop of equal mass and radius start from rest at the top of a ramp. They are released at the same time and roll without slipping down the ramp. Which one has the most total kinetic energy at the bottom?

A) The disk

B) The hoop

C) Both are the same.

C) Both are the same.

A disk and a hoop of equal mass and radius start from rest at the top of a ramp. They are released at the same time and roll without slipping down the ramp. Which one reaches the bottom of the ramp first?

A) The disk

B) The hoop

C) Both are the same

A) The disk

In the last lecture, we saw an example of a cylindrical object that does not roll down an inclined plane. What does this tell you about its moment of inertia?

A) Its moment of inertia is very large

B) Its moment of inertia is zero

C) Its moment of inertia is negative

D) This has nothing to do with its moment of inertia

A) Its moment of inertia is very large

• Can never be negative

What’s moment of inertia?

how easy it is to make it spin

Rank the effectiveness of the wrench at tightening the nut. That is, rank the

magnitude of the torque from greatest to least.

A) A > B > C > D

B) D > A > C > B

C) D = A > C > B

D) D = C > A > B

E) B = C > D > A

B) D > A > C > B

Three forces of equal magnitude act on a massless bar of length 1m as shown below. If the net torque about P is 10 Nm, what is the magnitude of the applied forces? The distances indicated below are measured from the pivot point P to the applied force, and the applied forces act perpendicular to the rod

18.2 N

The masseter muscle provides most of the force to close the jaw while biting. The bite force is exerted at the location indicated in the figure. Assume that there is no net torque in the jaw when you carefully and slowly bite down on a bite of food. How does the magnitude of the biting force compare to the muscle force in this situation?

A) The biting force is the same

B) The biting force is smaller

C) The biting force is larger

D) It’s not possible to tell

B) The biting force is smaller

When is an object in static equilibrium?

Net force is zero and Net torque is zero

• These conditions ensure no linear or rotational acceleration

What is periodic motion?

Motion that repeats itself at regular time intervals

What is a cycle?

One complete repetition of a periodic motion (Ex. one revolution in circular motion or one oscillation of a mass on a spring)

What’s Periode (T)?

Time required for one cycle of periodic motion

What’s frequency (f)?

Number of cycles per time

What is simple harmonic motion?

• One specific type of periodic motion

• The acceleration of the system is proportional to the displacement and acts in the opposite direction of the displacement

What is a common example of simple harmonic motion?

The motion of a mass on a spring

• The force is proportional to the displacement from equilibrium and always points towards the equilibrium position (Hooke’s law)

A simple pendulum is defined to have a _________, also known as the _________, which is suspended from a string of length L with negligible mass.

point mass; pendulum bob

In an ideal system with no work done by nonconservative forces, the total ___________ is conserved.

mechanical energy

What’s a damped oscillation?

An oscillation that runs down and stops

What’s a reason for dissipation of energy?

Non-conservative forces such as friction or air resistance

Losing energy means that the amplitude ________.

decreases

The non-conservative force impacts __________.

frequency

What’s an envelope?

Provides a border to the rapid oscillations

Underdamped

The system oscillates while the amplitude of the motion decays exponentially

• b < square root 4mk

Critically damped

The damping of an oscillator results in it returning as quickly as possible to its equilibrium position. Here, the system does not oscillate, but asymptotically approaches the equilibrium condition as quickly as possible

• b = square root 4mk

Which is most effective to get energy out of the system? (Underdamped, critically damped, or overdamped)

Critically damped

• Goes to zero as quickly as possible

Overdamped

As with critical damping, it the system may overshoot the equilibrium position, but it will not oscillate and it will reach equilibrium over a longer period of time; Friction so strong, it slows everything down

• b > square root 4mk

What does a response curve plot?

Plots the amplitude of a driven oscillator as a function of the external frequency

When driving an oscillation the amplitude also depends on the amount of _________.

damping in the system

The resonance amplitude becomes higher and narrower as the damping constant ________.

decreases

What’s a wave?

A disturbance traveling through a medium

• The medium produces an elastic restoring force when it is deformed allowing the wave to propagate

Basic mechanical waves are governed by _________.

Newton’s Laws

Mechanical waves transfer energy and momentum, without transferring ________.

mass

Some examples of mechanical waves are:

water waves, sound waves, seismic waves

The wave model is built around the idea of a _________.

traveling wave

What’s a traveling wave?

An organized disturbance traveling with a well-defined wave speed

What’s a transverse wave?

• Easiest type of wave to visualize

• The displacement of the medium is perpendicular to the direction of motion of the wave

In a longitudinal wave, the displacement is __________.

along the direction of wave motion

What type of waves are sound waves an example of?

Longitudinal waves

In a sound wave, the ________ and __________ are the quantities that oscillate.

density and pressure of the air

Water waves can be a combination of ________ and _________ waves.

transverse and longitudinal

Wave Pulse

● A single, localized disturbance traveling through the medium. Can be more intuitive to understand as it resembles a brief "moment" of disturbance.

● Has a well-defined speed and duration

Sinusoidal Wave

● A continuous, repeating wave with a smooth, regular oscillation, often described by a sine or cosine function.

● Most common wave type in nature, found in sound, light, and water waves.

● Easy to describe → connection to simple harmonic motion

Wave speed

How fast it travels through the medium

Wavelength

The distance over which the wave repeats.

Amplitude

The maximum displacement

What’s translational kinetic energy?

energy moving forward down ramp

What’s rotational kinetic energy?

energy spent spinning in a circle

Describe a hoop:

• Mass spread out further (Hollow)

• Larger moment of inertia - requires more energy to get it spinning

Describe a disk:

• Mass distributed evenly throughout

• Smaller moment of inertia - requires less energy to get it spinning

Mass per length

μ = m/L

A string with larger mass per length would have a ________ wave speed.

slower

As the tension in the string increases, the speed of waves on the string _________.

increases

Elastic property

tendency of the medium to return to their initial position when perturbed

Inertial property

tendency of the medium to resist changes

The speed of a longitudinal wave through a liquid or gas (ie. a sound wave) depends on the density of __________.

the fluid and the bulk modules B of the fluid

The amount of energy in a wave is related to its ___________ and __________.

amplitude and frequency

Intensity

It tells us how much energy a wave carries per unit area, and it is used to classify sound levels, laser beams, and many other wave phenomena

The constant k introduced for sinusoidal waves, is …

A. Boltzmann’s constant, with units: J/K

B. the electrostatic constant, with units: N m2 /c2

C. the force constant, with units: N/m

D. the wave number, with units: rad/m

E. the wavelength, with units: m

D. the wave number, with units: rad/m

For a wave pulse on a string to travel twice as fast, the string tension must be …

A. increased by a factor of 4.

B. increased by a factor of 2.

C. decreased to one half its initial value.

D. decreased to one fourth its initial value.

E. This is not possible. The pulse speed is always the same

A. increased by a factor of 4.

A sinusoidal wave travels along a lightweight string with wavelength λ1 and frequency f1. It reaches a heavier string, with a slower wave speed, and continues on with wavelength λ2 and frequency f2. Which is true?

A. λ2 = λ1 and f2 < f1

B. λ2 = λ1 and f2 > f1

C. λ2 > λ1 and f2 = f1

D. λ2 < λ1 and f2 = f1

E. λ2 < λ1 and f2 < f1

Consider circular ripples spreading on a pond → The lines that locate the crests are called _________.

wave fonts

What are wave fonts?

The crests of the wave. They are spaced one wavelength apart.

When a wave propagates through a medium, it ____________________.

reflects when it encounters the boundary of the medium

Fixed boundary condition

A wave pulse that reflects from a fixed in… has the same shape as before but is inverted.

Free boundary condition

A wave pulse reflecting from an end that is free to move… is not inverted.

In a discontinuous string, a part of the sting has a large _______________.

linear density and is connected to a part with a smaller linear density

If two waves combine to give a larger amplitude, this is ____________.

constructive interference