**Physics of Spool Mechanics**The spool of cable has a mass of \( m \) and a radius of gyration of \( k_c \). The tension in the cable \( T \) is a function of time \( t \), where \( t \) is in seconds. Neglect the mass of the unwound cable, and assume it is always at a constant radius.**Diagram Description:**The diagram illustrates a spool of cable resting on a horizontal surface. The spool has an outer diameter \( d_o \) and an inner diameter \( d_i \). A force due to tension \( T \) acts horizontally to the right on the cable wound around the spool.A coordinate system is implied with horizontal and vertical directions. The distance from the ground to the center of the spool is denoted as \( h \), and there is an angle \( \theta \) of 60° between the tension in the cable and the line perpendicular to the ground.**Parameters:**- Outer Diameter \( d_o = 1 \, \text{m} \)- Inner Diameter \( d_i = 0.5 \, \text{m} \)- Height \( h = 2.25 \, \text{m} \)- Radius of Gyration \( k_c = 0.77 \, \text{m} \)- Mass \( m = 100 \, \text{kg} \)- Tension in the cable \( T = 30t^3 + 77t \, \text{N} \)- Time \( t = 1.81 \, \text{s} \)- Force \( \vec{F} = 135t + 0j \, \text{N} \)**Exercises:**a) **Moment of Inertia of the Spool:** To find the moment of inertia \( I \) of the spool, we use the formula: \[ I = m k_c^2 \]b) **Angular Acceleration:** The angular acceleration \( \alpha \) of the wheel at time \( t \) can be computed using: \[ \alpha = \frac{\tau}{I} \] where \( \tau \) is the torque.c) **Cable Pulling Speed:** To determine how quickly the cable is being pulled at time \( t \),

(a) Write the expression for moment of inertia of the spool. I=mkc2

The spool of cable has a mass of m and a radius of gyration of ke. The tension in the cable T is a function of time t, when t is in seconds. Neglect the mass of the unwound cable, and assume it is always at a constant radius. a.) What is the moment of Inertia of the spool? b.) What is the angular acceleration of the wheel at t (Use + for the ccw direction)? c.) How quickly is the cable being pulled at time t (Use + for to the right) in m/s? do h d₁ 0 = 60° Variable do d h kc Ethe m T Value 1m 0.5 m 2.25 m 0.77 m 100 kg 30t³ +77t N 1.81 s 135i + 0) N

The spool of cable has a mass of m and a radius of gyration of ke. The tension in the cable T is a function of time t, when t is in seconds. Neglect the mass of the unwound cable, and assume it is always at a constant radius. a.) What is the moment of Inertia of the spool? b.) What is the angular acceleration of the wheel at t (Use + for the ccw direction)? c.) How quickly is the cable being pulled at time t (Use + for to the right) in m/s? do h d₁ 0 = 60° Variable do d h kc Ethe m T Value 1m 0.5 m 2.25 m 0.77 m 100 kg 30t³ +77t N 1.81 s 135i + 0) N

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Power Transmission Elements

It is defined as the energy transfer from one location to another location. The energy will start moving from the energy generation source to the energy applied position to obtain the work output. From this method, a large amount of electric energy moves from the power station to various electrical substations.

Question

**Physics of Spool Mechanics**

The spool of cable has a mass of \( m \) and a radius of gyration of \( k_c \). The tension in the cable \( T \) is a function of time \( t \), where \( t \) is in seconds. Neglect the mass of the unwound cable, and assume it is always at a constant radius.

**Diagram Description:**
The diagram illustrates a spool of cable resting on a horizontal surface. The spool has an outer diameter \( d_o \) and an inner diameter \( d_i \). A force due to tension \( T \) acts horizontally to the right on the cable wound around the spool.

A coordinate system is implied with horizontal and vertical directions. The distance from the ground to the center of the spool is denoted as \( h \), and there is an angle \( \theta \) of 60° between the tension in the cable and the line perpendicular to the ground.

**Parameters:**
- Outer Diameter \( d_o = 1 \, \text{m} \)
- Inner Diameter \( d_i = 0.5 \, \text{m} \)
- Height \( h = 2.25 \, \text{m} \)
- Radius of Gyration \( k_c = 0.77 \, \text{m} \)
- Mass \( m = 100 \, \text{kg} \)
- Tension in the cable \( T = 30t^3 + 77t \, \text{N} \)
- Time \( t = 1.81 \, \text{s} \)
- Force \( \vec{F} = 135t + 0j \, \text{N} \)

**Exercises:**

a) **Moment of Inertia of the Spool:**
To find the moment of inertia \( I \) of the spool, we use the formula:
\[
I = m k_c^2
\]

b) **Angular Acceleration:**
The angular acceleration \( \alpha \) of the wheel at time \( t \) can be computed using:
\[
\alpha = \frac{\tau}{I}
\]
where \( \tau \) is the torque.

c) **Cable Pulling Speed:**
To determine how quickly the cable is being pulled at time \( t \),

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