## Questions and Answers

What does the angle of banking on a road define?

The speed of the vehicle

In the context of a conical pendulum, what does the 'night time period' refer to?

The period of oscillation of the pendulum in the absence of daylight

What does the 'speed at highest lowest in midway' represent for a particle performing vertical motion?

Instantaneous speed at different points of vertical motion

What does the 'theorem of perpendicular axis' state about a rotating body?

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How does the principle of conservation of angular momentum relate to the kinetic energy of a rolling body?

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## Study Notes

### Banking of Roads

- Banking of roads is a technique used to ensure safe speed of vehicles on curved roads
- Banking allows vehicles to take turns at higher speeds without skidding or losing control

### Angle of Banking

- The angle of banking is the angle at which the road is tilted
- The expression for angle of banking can be derived as: tan(θ) = v^2 / (rg)

### Maximum Safe Speed

- The maximum safe speed of a vehicle on a banked road is directly proportional to the radius of the curvature of the road and the angle of banking
- The expression for maximum safe speed can be derived as: v = √(rg tan(θ))

### Conical Pendulum

- A conical pendulum is a weight attached to a string that moves in a circular motion
- The expression for the time period of a conical pendulum can be derived as: T = 2π √(l/g)

### Vertical Motion

- A particle performing vertical motion under gravity follows a parabolic path
- The expression for speed at the highest, lowest, and midway points of the motion can be derived using the equations of motion

### Rotational Motion

- The torque acting on a rotating body can be expressed as: τ = r x F
- The kinetic energy of a rotating body can be expressed as: K = (1/2) I ω^2

### Theorems of Rotational Motion

- The theorem of perpendicular axis states that the moment of inertia of a body about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two perpendicular axes in its plane
- The theorem of parallel axis states that the moment of inertia of a body about an axis parallel to its plane is equal to the moment of inertia about an axis through its center of mass plus the product of its mass and the square of the distance between the two axes

### Principle of Conservation of Angular Momentum

- The principle of conservation of angular momentum states that the total angular momentum of a closed system remains constant over time
- The kinetic energy of a rolling body can be expressed as the sum of the translational kinetic energy and the rotational kinetic energy

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## Description

Test your understanding of the expressions for safe speed of a vehicle on a banked road, angle of banking, angular speed of a vehicle on a banked road, period of a conical pendulum, speed at different points of vertical motion, and torque on a rotating body. This quiz covers various physics concepts related to road banking and pendulum motion.