1. A small fly wheel fitted to a motor with a moment of inertia of 80 kg m² slows down from 9000 rpm to 5500 rpm in 7.5 seconds.

For the fly wheel, calculate:
• The rate of deceleration which you can assume to be constant
• The braking torque.

2.If the energy used to heat up a block of 2kg of copper is 115.8 kJ, what is the temperature it was heated to if the starting temperature was 100oC and the specific heat capacity is 386 J/kgK.

1. V1 = 9000rev/min * 1min/60s * 6.28rad/rev = 942.5 rad/s.

V2 = 5500rev/min * 1min/60s * 6.28rad/rev. = 576 rad/s.

a. a = (V2-V1)/t

1. To find the rate of deceleration of the flywheel, we need to calculate the angular acceleration. Angular acceleration is defined as the change in angular velocity divided by the change in time:

Angular acceleration (α) = (ω2 - ω1) / t

Where:
- ω1 is the initial angular velocity in radians per second (9000 rpm = (9000/60) * 2π rad/s)
- ω2 is the final angular velocity in radians per second (5500 rpm = (5500/60) * 2π rad/s)
- t is the time in seconds (7.5 s)

Substituting the values into the formula:

α = ((5500/60) * 2π - (9000/60) * 2π) / 7.5

Simplifying, we get:

α = (5500 - 9000) * π / (60 * 7.5)

Now we can calculate the rate of deceleration (negative value since it is decelerating):

Rate of deceleration = -α

2. To find the braking torque of the flywheel, we can use the rotational analog of Newton's second law, which states that the torque applied to an object is equal to the moment of inertia multiplied by the angular acceleration:

Torque (τ) = moment of inertia (I) * angular acceleration (α)

Where:
- I is the moment of inertia of the flywheel (80 kg m², given in the problem)
- α is the angular acceleration (calculated in the first step)

Substituting the values into the formula:

τ = 80 * (-α)

Now we can calculate the braking torque.

2. To find the final temperature of the copper block, we can use the equation for heat energy:

Heat energy (Q) = mass (m) * specific heat capacity (c) * change in temperature (ΔT)

Where:
- Q is the heat energy (115.8 kJ, given in the problem; convert to J)
- m is the mass of the copper block (2 kg, given in the problem)
- c is the specific heat capacity of copper (386 J/kgK, given in the problem)
- ΔT is the change in temperature (final temperature - starting temperature)

First, convert the given heat energy from kilojoules to joules:

Q = 115.8 * 1000

Substituting the values into the equation:

115.8 * 1000 = 2 * 386 * (final temperature - 100)

Now solve for the final temperature:

(final temperature - 100) = (115.8 * 1000) / (2 * 386)

final temperature = [(115.8 * 1000) / (2 * 386)] + 100

Calculate the final temperature using the above equation.