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What is the value of tangential acceleration in U.C.M.?
Concept: Angular Acceleration
Obtain expressions of energy of a particle at different positions in the vertical circular motion .
Concept: Vertical Circular Motion Due to Earth’s Gravitation
A particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform the vertical circular motion, under gravity. The minimum speed of a particle is 5 m/s. Consider the following statements.
P) Maximum speed must be `5sqrt5` m/s.
Q) Difference between maximum and minimum tensions along the string is 60 N.
Select the correct option.
Concept: Circular Motion and Its Characteristics
A thin walled hollow cylinder is rolling down an incline, without slipping. At any instant, without slipping. At any instant, the ratio "Rotational K.E.: Translational K.E.: Total K.E." is ______.
Concept: Rotational Dynamics
Do we need a banked road for a two-wheeler? Explain.
Concept: Rotational Dynamics
Answer in brief:
Derive an expression which relates angular momentum with the angular velocity of a rigid body.
Concept: Conservation of Angular Momentum
Discuss the interlink between translational, rotational and total kinetic energies of a rigid object rolls without slipping.
Concept: Rolling Motion
A diver in a swimming pool bends his head before diving. It ______.
Concept: Moment of Inertia as an Analogous Quantity for Mass
A stone is tied to one end of a string. Holding the other end, the string is whirled in a horizontal plane with progressively increasing speed. It breaks at some speed because ______
Concept: Angular Momentum or Moment of Linear Momentum
During ice ballet, while in the outer rounds, why do the dancers outstretch their arms and legs.
Concept: Rotational Dynamics
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.
Concept: Moment of Inertia as an Analogous Quantity for Mass
A bucket containing water is tied to one end of a rope 5 m long and it is rotated in a vertical circle about the other end. Find the number of rotations per minute in order that the water in the bucket may not spill.
Concept: Rotational Dynamics
A flywheel of mass 8 kg and radius 10 cm rotating with a uniform angular speed of 5 rad/sec about its axis of rotation, is subjected to an accelerating torque of 0.01 Nm for 10 seconds. Calculate the change in its angular momentum and change in its kinetic energy.
Concept: Angular Momentum or Moment of Linear Momentum
What is a conical pendulum? Obtain an expression for its time period
Concept: Rotational Dynamics
Obtain an expression for maximum safety speed with which a vehicle can be safely driven along a curved banked road.
Concept: Rotational Dynamics
When the bob performs a vertical circular motion and the string rotates in a vertical plane, the difference in the tension in the string at horizontal position and uppermost position is ______.
Concept: Vertical Circular Motion
Calculate the moment of inertia of a uniform disc of mass 10 kg and radius 60 cm about an axis perpendicular to its length and passing through its center.
Concept: Moment of Inertia as an Analogous Quantity for Mass
An electron in an atom is revolving round the nucleus in a circular orbit of radius 5.3 × 10-11 m with a speed of 3 × 106 m/s. Find the angular momentum of electron.
Concept: Angular Momentum or Moment of Linear Momentum
If friction is made zero for a road, can a vehicle move safely on this road?
Concept: Applications of Uniform Circular Motion
Derive expressions for the linear velocity at the lowest position, mid-way position and top-most position for a particle revolving in a vertical circle, if it has to just complete circular motion without string slackening at the top.
Concept: Vertical Circular Motion
