There is a spot of paint on the front wheel of the bicycle. Take the position of the spot at time t=0 to be at angle θ=0 radians with respect to an axis parallel to the ground (and perpendicular to the axis of rotation of the tire) and measure positive angles in the direction of the wheel's rotation. What angular displacement θ has the spot of paint undergone between time 0 and 2 seconds?

Answers

Answer 1

Here is the missing information.

An exhausted bicyclist pedal somewhat erraticaly when exercising on a static bicycle. The angular velocity of the wheels takes the equation ω(t)=at − bsin(ct) for t≥ 0, where t represents time (measured in seconds), a = 0.500 rad/s2 , b = 0.250 rad/s and c = 2.00 rad/s .

Answer:

0.793 rad

Explanation:

From the given question:

The angular velocity of the wheel is expressed by the equation:

[tex]\omega (t) =\dfrac{d\theta}{dt}[/tex]

The angular velocity of the wheels takes the description of the equation ω(t)=at−bsin(ct)

SO;

[tex]\dfrac{d \theta}{dt} = at - b \ sin \ ct[/tex]

dθ = at dt - (b sin ct) dt

Taking the integral of the above equation; we have:

[tex]\int \limits^{\theta}_{0} \ d \theta = \int \limits ^{t=2}_{0} at \ dt - (b \ sin \ ct) \dt[/tex]

[tex][\theta] ^{\theta}_{0} = a \bigg [\dfrac{t^2}{2} \bigg]^2_0 - \bigg[ -\dfrac{b}{c} \ cos \ ct \bigg] ^2_0[/tex]

where;

a = 0.500 rad/s2 ,

b = 0.250 rad/s and

c = 2.00 rad/s

[tex]\theta = (0.500 \ rad/s^2 ) \bigg [\dfrac{(2s)^2}{2} \bigg] - \bigg[ -\dfrac{0.250 \ rad/s}{2.00 \ rad/s} \ cos \ (2.00 \ rad/s )( 2.00 \ s) \bigg] - \bigg [ \dfrac{0.250 \ rad/s}{2.00 \ rad/s}\bigg ] cos 0^0[/tex]

[tex]\mathbf{\theta = 0.793 \ rad}[/tex]

Hence, the angular displacement after two seconds = 0.793 rad


Related Questions

A 30kg dog runs at a speed of 15 m/s. What is the dog's Kinetic energy?

Answers

A :-) KE = 1 by 2 mv^2
Given - m = 30 kg
v = 15 m/s ( speed = velocity )
Solution -
KE = 1 by 2 mv^2
KE = 1 by 2 x 30 x 15
( cut 2 and 30 because 2 x 15 = 30 )
KE = 15 x 15
KE = 225 J

.:. The kinetic energy ( KE ) = 225 J.

Bicycle A with mass 40 Kg is traveling with a velocity of 4 m/s and Bicycle B with mass 20 Kg is traveling with a velocity of 2m/s. The two bicycles have kinetic energy
Calculate it and state which bicycle has higher energy and why?

Answers

Answer:

bicycle A has a greater K.E.

Explanation:

K.E = 1/2mv²

bicycle A = 1/2 × 40 × 4² = 320J

bicycle B = 1/2 × 20 × 2² = 100J

bicycle A has a greater K.E. because it has bigger mass and moves with faster velocity

Who could explain the phenomenom of interference of light?​

Answers

Answer:

When the waves reflected from the inner and outer surface combine they will interfere with each other, removing or reinforcing some parts of white light by destructive or constructive interference. ... This results in color.

Explanation:

this is what we studied

so basically  there is like a surface

and 2 different waves coming out of the same source

they will combine and start removing parts of the white light (which originally consists of 6 to 7 colors)

results in showing these colors

Which two explanations are based on personal beliefs?

I A. Certain mineral crystals have properties that help protect the

body from illness.

IB. A constellation's position in the night sky can be used to predict

events in a person's life.

I C. Medical data gathered over many years show that lack of

adequate sleep causes health problems.

D. Observations using microscopes reveal that all known organisms

are composed of tiny structures called cells.

I E. Data gathered during experiments show that there is an inverse

relationship between the force of gravity and distance.

Answers

Answer:

The correct options are A and B

Explanation:

Personal beliefs can be described as beliefs that have not been scientifically proven. These beliefs are generally as a result of religion, culture or tradition. Scientifically in theory, these beliefs lack clear path of possibility. For example, being in possession of certain mineral crystals in order to help protect the body against illness have a little possibility of being scientifically (in theory) explained. There is also no scientific evidence to support this claim.

There is also no scientific evidence to support the idea of the constellation's position to predict  events in a person's life. This also has little possibility of being theoretically explained in science.

It should however be noted that there are exceptions/coincidences that suggest these events happen as it has been listed in the two options.

Answer: A and B!

Explanation: Just took the quiz.

A ball projected horizontally from 180meter tall building lands 450 meter away from the foot of the building find velocity of the ball after leafs the building find velocity of the ball after it leafs the building​

Answers

Answer:

74.28 m/s

Explanation:

In this case, it is a zero launch angle in that the object is launched horizontally at a height H.

The formula to apply is:

[tex]R=v_o*\sqrt{\frac{2H}{g} }[/tex]

where

R= range, 450 m

H= height of building ,180 m

g= 9.81

vo= ? initial velocity

Applying the values to the equation;

[tex]450 = v_o*\sqrt{\frac{2*180}{9.81} } \\\\450=v_o*\sqrt{36.70} \\\\450=v_o*6.06\\\\450/6.06 = v_o\\\\74.28 m/s=v_o[/tex]

what is the process of subduction

Answers

Answer:

Subduction is a geological process that takes place at convergent boundaries of tectonic plates where one plate moves under another and is forced to sink due to high gravitational potential energy into the mantle. Regions where this process occurs are known as subduction zones.

A spacecraft orbiting Earth is both moving forward and

a. at terminal velocity
b. experiencing resistance
c. weightless
d. towards earth

Answers

Answer:  (A) At terminal velocity ...

Explanation:

At terminal velocity

I have been trying to do number 2 and I just don’t know what the answer is if you can help me thank you so mush

Answers

Answer:

Strong Positive Linear Line Correlation

Explanation:

According to the diagram, there is a strong positive linear line correlation between velocity and distance of galaxies. Hubble showed that galaxies are receding away from people with a velocity that is proportional to their distance from people more distant galaxies recede faster than nearby galaxies.

About the diagram: Velocity is the distance relation among extra-galactic nebulae. Radial velocities is corrected for solar motion, are plotted against distances estimated from involved stars and mean luminosities of nebulae in a cluster. The black discs and full line represent the solution for solar motion by using the nebulae individually; the circles and broken line represent the solution combining the nebulae into groups; the cross represents the mean velocity corresponding to the mean distance of 22 nebulae whose distances could not be estimated individually.

Why is it hard to respond with action at times?

Answers

Yes it can be very hard
Usually people would sometimes need an example as an action

The energy stored inside a battery is best described as...
a. potential energy
b. Elastic
c. Mechanical
d. Kinetic

Answers

Answer:

potential energy

Explanation:

by the sun

Two identical spheres (of equal mass) a distance of 10 meters apart exert a force of gravity of 0.00050 N on each other. What are their masses?

Answers

Answer:

The gravitational force between two objects is written as:

F = G*m1*m2/r^2

Where:

G = 6.67*10^(-11) m^3/kg*s

m1 and m2 are the masses of the objects.

r is the distance between the objects.

In this case, we know that:

F = 0.0005 N

r = 10m

and because the two spheres are identical, we have that:

m1 = m2 = M

then we have the equation:

0.0005 N = (6.67*10^(-11) m^3/kg*s)*(M^2/(10m)^2)

0.0005 N*(10m)^2/(6.67*10^(-11) m^3/kg*s) = M^2

√( 0.0005 N*(10m)^2/(6.67*10^(-11) m^3/kg*s) ) = M = 27,379.3 kg

The mass of each sphere is 27,379.3 kg

Phich instrument can be used to give a direct measurement of the mass of a rock on moon

Answers

Answer:

you can use a balance

Explanation:

when you tend to measure something you are using your brain so why dont you use your brain dimwitt

3. What are the forces present on the rope?​

Answers

Answer:

The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension, T. When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object: T = mg.

An 856 kg drag race car accelerates from rest to 105 km/h in .934s. What change in momentum does the force produce? Answer in units of kg • m/s

Part 2: what average force is exerted on the car? Answer in N

Answers

Hello!

Topic: Dinamic

Value to calculate: Force

First, we have to calculate the aceleration, for that, lets aplicate the formula:

[tex]\boxed{a=\frac{V-Vi}{t} }[/tex]

How the final velocity is in km/h, we have to convert it on m/s, so:

m/s = km/h / 3,6

m/s = 105 / 3,6

m/s = 29,16

Then, lets replace formula according problem information:

[tex]a = \dfrac{29,16m/s-0m/s}{0,934s}[/tex]

[tex]a =31,22\ m/s^{2}[/tex]

Now, how we have the aceleration, lets applicate second law of newton for calculate the force produced:

[tex]\boxed{F=ma}[/tex]

Replace and resolve it:

F = 856 kg * 31,22 m/s^2

F = 26724,32 kg * m/s^2

Then the force is of 26724,32 kg * m/s^2

But how we know an 1 kg * m/s^2 = 1 N

Then the average of the force is of 26724,32 N  

(1) The change in momentum of race car is 89880 kg-km/h.

(2) The average force exerted on the car is of 96231.26 N.

Given data:

The mass of race car is, m = 856 kg.

The initial speed of car is, u = 0 km/h.

The final speed of car is, v = 105 km/h.

The time interval is, t = 0.934 s.

1)

The change in the impact due to average force is known as momentum change. The expression for the change in momentum is given as follows,

[tex]\Delta P = m(v-u)[/tex]

Solving as,

[tex]\Delta P = 856 \times (105-0)\\\\\Delta P = 89880 \;\rm kg.km/h[/tex]

Thus, we can conclude that the change in momentum of race car is 89880 kg-km/h.

2)

Now, use the concept of impulse-momentum which says that the impulse is equal to change in momentum. Which means,

[tex]I = \Delta P[/tex]

And impulse is,

[tex]F \times t = \Delta P\\\\F = \dfrac{\Delta P}{t}[/tex]

Solving as,

[tex]F = \dfrac{89880}{0.934}\\\\F = 96231.26 \;\rm N[/tex]

Thus, we can conclude that the average force exerted on the car is of 96231.26 N.

Learn more about the impulse-momentum theorem here:

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Answer:

One arm row: Latissmus Dorsi (Lat)

Dumbell flys: Shoulders

Machine back press: pectorals

Push downs: Triceps

Explanation:

gsjsjsjjshsjds

What is the pigment in the leaves called?
1.Chloroplasts
2.Green
3.Stroma
4.Chlorophyll

Answers

Answer: D: Chloroplasts

Explanation:

Answer: d

Explanation:

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Answer:

earth is 4.54 billion years old

for an organism to survive they would have to change ( mutate )

A mutation is any permenant change in dna of a gene or chromosome

some mutations are bad and some can be good

Explanation:

An object is dropped into a beaker containing liquid the object drops to the bottom of the beaker therefore

Answers

An object is dropped into a beaker containing liquid the object drops to the bottom of the beaker therefore the density of the object is greater than that of  liquid inside the beaker.

What is density?

The density of a substance indicates how dense it is in a given area. Mass per unit volume is the definition of a material's density. In essence, density is a measurement of how closely stuff is packed. It is a particular physical characteristic of a specific thing.

The Greek scientist Archimedes made the discovery of the density principle. The letter D can also be used to signify density instead of the symbol ρ .

According to Archimedes  principle, if an object is dropped into a beaker containing liquid the object drops to the bottom of the beaker, the density of the object is greater than that of the liquid inside the beaker.

Learn more about density here:

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