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2 years ago

The relationship between linear velocity and angular velocity

Physics

1 answer:

bonufazy [111]2 years ago

7 0

In linear motion , when a body moves with uniform velocity , in time t , its linear displacement will be ;

S = r∅ S = vt

r∅ = vt

r.∅ / t = v

v = rw

where ∅ = 90° is the angle between between radius vector r and angular velocity w (omega )

In case ∅ ≠ 90° , we can write v = r w sin∅

It gives us v = w× r

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particle of mass 59 g and charge 51 µC is released from rest when it is 32 cm from a second particle of charge −14 µC. Determine

AleksAgata [21]

Answer:

The initial acceleration of the 59g particle is $1062.7\frac{m}{s^{2}}$

Explanation:

Newton's second laws relates acceleration (a), net force(F) and mass (m) in the next way:

$F=ma$ (1)

We already know the mass of the particle so we should find the electric force on it to use on (1), the magnitude of the electric force between two charged objects by Columb's law is:

$F=k\frac{\mid q_{1}q_{2}\mid}{r^{2}}$

with q1 and q2 the charge of the particles, r the distance between them and k the constant $k=9.0\times10^{9}\,\frac{Nm^{2}}{C^{2}}$ . So:

$F=(9.0\times10^{9})\frac{\mid (51\times10^{-6})(-14\times10^{-6})\mid}{0.32^{2}}$

$F=62.7 N$

Using that value on (1) and solving for a

$a=\frac{F}{m}=\frac{62.7}{0.059}=1062.7\frac{m}{s^{2}}$

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3 years ago

g An astronaut must journey to a distant planet, which is 189 light-years from Earth. What speed will be necessary if the astron

Butoxors [25]

Answer:

The value is $v = 2.999 *10^{8} \ m/s$

Explanation:

From the question we are told that

The time taken to travel to the planet from earth is $t = 189 \ light-years$

The time to be spent on the ship is $t_{s} = 12 \ years$

Generally speed can be obtained using the mathematical relation represented below

$t_s = 2 * t * \sqrt{1 - \frac{v^2}{c^2 } }$

The 2 in the equation show that the trip is a round trip i.e going and coming back

=> $12 = 2 * 189 * \sqrt{1 - \frac{v^2}{(3.0*10^{8})^2 } }$

=> $v = 2.999 *10^{8} \ m/s$

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2 years ago

Resistor is made of a very thin metal wire that is 3.2 mm long, with a diameter of 0.4 mm. What is the electric field inside thi

Zanzabum

Complete question:

Resistor is made of a very thin metal wire that is 3.2 mm long, with a diameter of 0.4 mm. What is the electric field inside this metal resistor? If the potential difference due to electric field between the two ends of the resistor is 10 V.

Answer:

The electric field inside this metal resistor is 3125 V/m

Explanation:

Given;

length of the wire, L = 3.2 mm = 3.2 x 10⁻³ m

diameter of the wire, d = 0.4 mm = 0.4 x 10⁻³ m

the potential difference due to electric field between the two ends of the resistor, V = 10 V

The electric field inside this metal resistor is given by;

ΔV = EL

where;

ΔV is change in electric potential

E = ΔV / L

E = 10 / (3.2 x 10⁻³ )

E = 3125 V/m

Therefore, the electric field inside this metal resistor is 3125 V/m

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