Chapter1. Rotational Dynamics 1. A diver in a swimming pool bends his head before diving. It a) Increases his linear velocity b) Decreases his angular velocity c) Increases his moment of inertia d) Decreases his moment of inertia
Ans: d) Decreases his moment of inertia
2. The angular momentum of a system of particles is conserved a) When no external force acts upon the system b) When no external torque acts upon the system c) When no external impulse acts upon the system d) When axis of rotation remains the same
Ans: b) When no external torque acts upon the system
3. A stone is tied to one end of a string. Holding the other end, the string is whirled in ahorizontal plane with progressively increasing speed. It breaks at some speed because a) Gravitational forces of the earth is greater than the tension in string b) The required centripetal force is greater than the tension sustained by the string c) The required centripetal force is lesser than the tension in the string d) The centripetal force is greater than the weight of the stone
Ans: b) The required centripetal force is greater than the tension sustained by the string
4. A 500 kg car takes a round turn of radius 50m with a velocity of 36 km/hr. The centripetal force is a) 250N b) 750N c) 1000N d) 1200N
Ans: c) 1000N
Very Short Answer 1. Find the radius of gyration of a uniform disc about an axis perpendicular to its plane and passing through its center. 2. Does the angle of banking depend on the mass of the vehicle? 3. During ice ballet, while in the outer rounds, why do the dancers outstretch their arms and legs 4. State the principle of conservation of angular momentum. 5. Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, then what is the ratio of their angular velocity.
Short Answer: 1) Derive an expression for kinetic energy of a rotating body with uniform angular velocity. 2) Obtain an expression for the torque acting on a rotating body with constant angular acceleration. 3) Derive an expression for the difference in tensions at highest and lowest point for a particle performing vertical circular motion. 4) Obtain an expression for the angular momentum of a body rotating with uniform angular velocity
Long Answer: 1) State and explain the theorem of parallel axes. 2) What is a conical pendulum? Obtain an expression for its time period 3) Obtain an expression for maximum safety speed with which a vehicle can be safely driven along a curved banked road OR Show that the angle of banking is independent of mass of vehicle.
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