Express the dimensional formulas for the following physical quantities: a) linear momentum b) force c) pressure d) torque e) angular momentum f) kinetic energy

a) Linear momentum: [M][L][T]^-1
b) Force: [M][L][T]^-2
c) Pressure: [M][L]^-1[T]^-2
d) Torque: [M][L]^2[T]^-2
e) Angular momentum: [M][L]^2[T]^-1
f) Kinetic energy: [M][L]^2[T]^-2

a) Linear momentum

Linear momentum is defined as the product of mass and velocity. Mass is measured in kilograms (kg), and velocity is measured in meters per second (m/s). Therefore, the dimensional formula for linear momentum is:

```
p = mv
```

where:

- p is linear momentum (kg m/s)
- m is mass (kg)
- v is velocity (m/s)

b) Force

Force is defined as the rate of change of momentum. Momentum is measured in kg m/s, and time is measured in seconds (s). Therefore, the dimensional formula for force is:

```
F = dp/dt
```

where:

- F is force (N)
- p is linear momentum (kg m/s)
- t is time (s)

c) Pressure

Pressure is defined as force per unit area. Force is measured in newtons (N), and area is measured in square meters (m^2). Therefore, the dimensional formula for pressure is:

```
P = F/A
```

where:

- P is pressure (Pa)
- F is force (N)
- A is area (m^2)

d) Torque

Torque is defined as the product of force and the distance from the axis of rotation. Force is measured in newtons (N), and distance is measured in meters (m). Therefore, the dimensional formula for torque is:

```
τ = Fr
```

where:

- τ is torque (Nm)
- F is force (N)
- r is distance from the axis of rotation (m)

e) Angular momentum

Angular momentum is defined as the product of moment of inertia and angular velocity. Moment of inertia is measured in kilogram meters squared (kg m^2), and angular velocity is measured in radians per second (rad/s). Therefore, the dimensional formula for angular momentum is:

```
L = Iω
```

where:

- L is angular momentum (kg m^2/s)
- I is moment of inertia (kg m^2)
- ω is angular velocity (rad/s)

f) Kinetic energy

Kinetic energy is defined as the work done to accelerate an object from rest to a given velocity. Work is measured in joules (J), and velocity is measured in meters per second (m/s). Therefore, the dimensional formula for kinetic energy is:

```
K = 1/2 mv^2
```

where:

- K is kinetic energy (J)
- m is mass (kg)
- v is velocity (m/s)

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