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3 years ago

The relationship between linear velocity and angular velocity

Physics

1 answer:

bonufazy [111]3 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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Tarzan, whose mass is 94 kg, is hanging at rest from a tree limb. Then he lets go and falls to the ground. Just before he lets g

zalisa [80]

Answer:

(a) 6.26 m/s

(b) ‭-2,118.76 J

Explanation:

Here we have

Tarzan's mass, m = 94 kg

Height of feet above ground, h₁ = 2.0 m

Height of center of mass above ground = 2.8 m

Height of center of mass on the ground, h₂ = 2.8 - 2.0 = 0.8 m

Height of center of mass in the crouched position, h₃ = 0.5 m

(a) The speed at the instant just before Tarzan's feet touches the ground is given by;

v² = u² + 2·g·h₁

v = Speed at the instant just before Tarzan's feet touches the ground

u = Initial speed = 0 m/s while hanging from the tree

g = Acceleration due to gravity

Therefore, v² = 2·g·h₁ = 2 × 9.8 × 2 = 39.2 m²/s²

∴ v = √(39.2 m²/s²) = 6.26 m/s

(b) Here we have

Just before Tarzan's feet touches the ground internal energy is given by;

Initial Internal energy = K.E. + P.E. = m·g·h₂+ 0.5·m·v²

= 94 × 9.8 × 0.8 + 0.5 × 94 × 39.2 = ‭2,579.36 J

When in the crouched position, the final internal energy is given by;

m·g·h₃ = 94 × 9.8 × 0.5 = 460.6 J

Therefore net change in internal energy, ΔU is given by

ΔU = Final internal energy - Initial internal energy

ΔU = 460.6 J - 2,579.36 J = ‭-2,118.76 J.

4 0

3 years ago

A noisy toy is placed in a glass jar. All the air is then slowly removed from the jar. How does this affect the sound you hear?

MariettaO [177]

The sound would decrease because the sound waves have nothing to bounce against.

8 0

3 years ago

A particle of mass 73 g and charge 67 µC is released from rest when it is 47 cm from a second particle of charge −25 µC. Determi

stich3 [128]

Answer:

933.804423995 m/s²

Explanation:

$q_1$ = Charge on particle 1 = 67 µC

$q_2$ = Charge on particle 2 = -25 µC

r = Distance between the particles = 47 cm

k = Coulomb constant = $8.99\times 10^{9}\ Nm^2/C^2$

m = Mass of particle = 73 g

Electric force is given by

$F=\dfrac{kq_1q_2}{r^2}\\\Rightarrow F=\dfrac{8.99\times 10^{9}\times -25\times 10^{-6}\times 67\times 10^{-6}}{0.47^2}\\\Rightarrow F=-68.1677229516\ N$

The magnitude of force is 68.1677229516 N

Acceleration is given by

$a=\dfrac{F}{m}\\\Rightarrow a=\dfrac{68.1677229516}{0.073}\\\Rightarrow a=933.804423995\ m/s^2$

The acceleration is 933.804423995 m/s²

8 0

3 years ago

A free-falling golf ball strikes the ground and exerts a force on it. Which sentences are true about this situation? A golf ball

Harlamova29_29 [7]

Answer:

The ground exerts an equal force on the golf ball

Explanation:

Third's Newton Law states that:

"When an object A exerts a force on an object B, then object B exerts an equal and opposite force on object A".

In this problem, object A is the golf ball while object B is the ground, so we can say that:

- the golf ball exerts a force on the ground

- the ground exerts an equal and opposite force on the golf ball

8 0

3 years ago

Read 2 more answers

Of the more than 2,000 known minerals approximately 95% of them belong to what mineral group?

Temka [501]

Your answer is Silicates.

5 0

3 years ago