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Excellence Academy, Subject:- Physics, , Class:- 12th, , Faculty:- Prof. Dinesh Satpute, Date:- 11th April 2022, , Question Bank, Syllabus: Rotational Dynamics, Question, Number, 1, 2, 3, 4, 5, 1, 2, 3, 4, , 5, , 6, 7, 1, 2, 3, , 4, , Question, Part A, Define angular velocity and state its unit., Define Uniform Circular Motion (UCM)., Define conical pendulum., State the factors that affects the angle of banking., Define Moment of Inertia of a body, Part B, Distinguish between centripetal force and centrifugal force, A racing car completes 5 rounds of a circular track in 2 minutes., Find the radius of the track if the car has uniform centripetal, acceleration of π2 ms-2., Ans:- Radius = 144m, Do we need a banked road for a two-wheeler? Explain., What is the banking of roads? Why it is necessary?, A motor cyclist is to undertake horizontal circles inside the, cylindrical wall of a well of inner radius 4m. Coefficient of static, friction between the tyres and the wall is 0.4. Calculate the, minimum speed and frequency necessary to perform this stunt., (use g = 10m/s-2), Minimum speed = 10m/s, Minimum frequency = 0.4Hz, Define radius of gyration and give its physical significance., State the theorem of perpendicular axes., Part C, Derive an equation for maximum safe speed with which vehicle, should move along a curved horizontal road., Derive an expression for most safe speed of a vehicle on a curved, banked road ignoring friction., Define period of a conical pendulum and obtain an expression for, its period., A circular race course track has a radius of 500m and is banked at, 10o. The coefficient of static friction between the tyres of a vehicle, and the road surface is 0.25. Compute, 1. The maximum speed to avoid slipping, , Marks, 1, 1, 1, 1, 1, 2, 2, 2, 2, , 2, , 2, , 3, 3, 3, , 3

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5, 6, 7, 8, , 9, , 1, 2, , 3, 4, 5, , 2. The optimum speed to avoid wear and tear of the tyres, Answer:- Vmax = 46.75 m/s, Voptimum = 29.39 m/s, Derive an expression for kinetic energy of a body rotating with, uniform angular velocity, State and prove the theorem of parallel axes, Obtain an expression for torque acting on body rotating with, uniform angular acceleration., Calculate the M.I. of a solid sphere of mass 10kg and radius 0.5m,, rotating about an axis passing through a point at a distance of 0.2m, from the centre of the sphere., The speed of rotation of the body increases from 60rpm to 9rpm, in 1 minute. Calculate the torque acting on the body, if its moment, of inertia is 500kgm2., Part D, Derive an expression for minimum speed required by a vehicle, driven in horizontal circles of a vertical cylindrical wall., Draw a diagram showing all components of forces acting on a, vehicle moving on a banked curved road. Write the necessary, equation for maximum safe speed., Draw a diagram showing all components of forces acting on a, vehicle moving on a banked curved road. Write the necessary, equation for minimum speed., Obtain expressions of energy of a particle at different positions in, the vertical circular motion., Derive the relation between angular momentum and angular, velocity of a rigid body. State the SI unit and dimensions of angular, momentum, , 3, 3, 3, 3, , 3, , 4, 4, , 4, 4, 4