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#rotational-motion
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#kinetic-energy
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#angular-impulse
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#physics
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A solid disc of mass ￼ and radius ￼ is rotating at 120 revolutions per minute. Calculate
(i) It's Kinetic energy (2 marks)
Joules
(ii) Angular Impulse as it is brought to rest in 3s?

Feb 1

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Feb 1

To calculate the kinetic energy of the rotating disc, we need to know the moment of inertia of the disc. The moment of inertia of a solid disc is given by the formula:

I = (1/2) * m * r^2

where m is the mass of the disc and r is the radius of the disc.

Given that the mass of the disc is ￼ and the radius is ￼, we can substitute these values into the formula to find the moment of inertia:

I = (1/2) * (￼) * (￼)^2 = ￼

Next, we need to convert the rotational speed from revolutions per minute to radians per second. Since there are 2π radians in one revolution, we can use the following conversion factor:

1 revolution/minute = (2π radians/1 revolution) * (1 minute/60 seconds) = π/30 radians/second

Therefore, the angular velocity of the disc is:

ω = (120 revolutions/minute) * (π/30 radians/revolution) = 4π radians/second

The kinetic energy of the rotating disc is given by the formula:

KE = (1/2) * I * ω^2

Substituting the values we found earlier:

KE = (1/2) * (￼) * (4π)^2 = ￼

So the kinetic energy of the rotating disc is ￼ Joules.

To calculate the angular impulse, we need to know the change in angular momentum and the time taken for this change. Since the disc is brought to rest, the change in angular momentum is equal to the initial angular momentum. The initial angular momentum of the disc is given by:

L = I * ω

Substituting the values we found earlier:

L = (￼) * (4π) = ￼

The angular impulse is given by the formula:

Impulse = change in angular momentum = initial angular momentum

Therefore, the angular impulse is ￼.

Since the time taken for the change is 3 seconds, the angular impulse is ￼ radians/second.

Note: The values of mass and radius were not provided in the question, so I used placeholders (￼ and ￼) to represent these values. Please substitute the actual values to get the final answer.

I = (1/2) * m * r^2

where m is the mass of the disc and r is the radius of the disc.

Given that the mass of the disc is ￼ and the radius is ￼, we can substitute these values into the formula to find the moment of inertia:

I = (1/2) * (￼) * (￼)^2 = ￼

Next, we need to convert the rotational speed from revolutions per minute to radians per second. Since there are 2π radians in one revolution, we can use the following conversion factor:

1 revolution/minute = (2π radians/1 revolution) * (1 minute/60 seconds) = π/30 radians/second

Therefore, the angular velocity of the disc is:

ω = (120 revolutions/minute) * (π/30 radians/revolution) = 4π radians/second

The kinetic energy of the rotating disc is given by the formula:

KE = (1/2) * I * ω^2

Substituting the values we found earlier:

KE = (1/2) * (￼) * (4π)^2 = ￼

So the kinetic energy of the rotating disc is ￼ Joules.

To calculate the angular impulse, we need to know the change in angular momentum and the time taken for this change. Since the disc is brought to rest, the change in angular momentum is equal to the initial angular momentum. The initial angular momentum of the disc is given by:

L = I * ω

Substituting the values we found earlier:

L = (￼) * (4π) = ￼

The angular impulse is given by the formula:

Impulse = change in angular momentum = initial angular momentum

Therefore, the angular impulse is ￼.

Since the time taken for the change is 3 seconds, the angular impulse is ￼ radians/second.

Note: The values of mass and radius were not provided in the question, so I used placeholders (￼ and ￼) to represent these values. Please substitute the actual values to get the final answer.