What are the fastest spinning objects known in the universe?

Consider a motor that exerts a constant torque of 25.0 N⋅m to a horizontal platform whose moment of inertia is 50.0 kg⋅m2 . Assu

Step2247 [10]

To solve this exercise it is necessary to apply the concepts related to Work and Kinetic Energy. Work from the rotational movement is described as

$W=\tau \Delta\theta$

In the case of rotational kinetic energy we know that

$KE = \frac{1}{2}I\omega^2$

PART A) $\theta$ is given in revolutions and needs to be in radians therefore

$\theta = 12rev(\frac{2\pi rad}{1rev})$

$\theta = 24\pi rad$

Replacing in the work equation we have to

$W=\tau \Delta\theta$

$W= (25)(24\pi)$

$W = 1884.95J$

PART B) From the torque and moment of inertia it is possible to calculate the angular acceleration and the final speed, with which the kinetic energy can be determined.

$\tau = I \alpha$

Rearrange for the angular acceleration,

$\alpha = \frac{\tau}{I}$

$\alpha = \frac{25}{50}$

$\alpha = 0.5rad/s$

From the kinematic equations of angular motion we have,

$\omega_f^2=\omega_i^2+2\alpha\theta$

$\omega_f^2=0+2*0.5*24\pi$

$\omega_f=\sqrt{0+2*0.5*24\pi}$

$\omega_f = 8.68rad/s$

In this way the rotational kinetic energy would be given by

$KE = \frac{1}{2}I\omega_f^2$

$KE = \frac{1}{2}(50)(8.68)^2$

$KE = 1883.56J$

3 0

3 years ago

Read 2 more answers

Plz help me find the answers

san4es73 [151]

Answer: Plastids are the site of manufacture and storage of important chemical compounds used by the cells of autotrophic eukaryotes

Explanation:

6 0

3 years ago

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What happens when the Earth’s plates pull away from each other?

yan [13]

Volcanoes start to erupt because of the magnetic field.

5 0

3 years ago

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A truck, initially at rest, rolls down a frictionless hill and attains a speed of 2 m/s at the bottom. To achieve a speed of 6 m

faust18 [17]

Answer:

so the height will be increased by 9 times

Explanation:

The truck is in its pontential energy at rest

The potential energy is converted to kinetic energy when in motion

Given that,

h = height of the hill

m = mass of the truck

g = acceleration due to gravity

v = velocity of the truck at the bottom of the hill.

At the top of the hill,

Potential energy(PE) = mgh

Kinetic energy(KE) = 0

Total energy, E = PE + KE = mgh + 0 = mgh____(1)

At the bottom of the hill :

Potential energy, PE = 0

Kinetic energy,KE = (1/2)mv²

Total energy, E = PE + KE

= 0 + (1/2)mv²_____(2)

In law of conservation of energy,

(1) = (2)

mgh = (1/2)mv²

h = (1/2g)v²

given,

v = 2 m/s

g = 9.81 m/s²

h = (1/2(9.81)) × 2²

h = 0.20 m

so,

if v = 6 m/s

h = (1/2(9.81)) × 6²

h = 1.83 m

from the first h = 0.20m and the second h = 1.83m

1.83m / 0.20m

= 9.15

so the height will be increased by 9 times

5 0

4 years ago

What is the total resistance of 3 resistors of 3ohms added together in series?

san4es73 [151]

In series, you just add them: R1 + R2 + R3 = Total R

8 0

3 years ago