Physics: Banking of Roads and Conical Pendulum Expressions Quiz

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