Rotational Dynamics Physics - Rotational Dynamics

State the formula for moment of inertia of solid sphere about an axis passing through its center.

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 centre.

Define uniform circular motion.

What is the value of tangential acceleration in U.C.M.?

If friction is made zero for a road, can a vehicle move safely on this road?

A motor cyclist (to be treated as a point mass) is to undertake horizontal circles inside the cylindrical wall of a well of inner radius \(4 m\). The co-efficient of static friction between tyres and the wall is 0.2 . Calculate the minimum speed and period necessary to perform this stunt.

Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length.

State the law of conservation of angular momentum and explain with a suitable example.

A stone of mass \(5 kg\), tied to one end of a rope of length \(0.8 m\), is whirled in a vertical circle. Find the minimum velocity at the highest point and at the midway point. \(\left[g=9.8 m / s ^2\right.\) ]

A racing car completes 5 rounds on a circular track in 2 minutes. Find the radius of the track if the car has uniform centripetal acceleration of \(n ^2 m / s ^2\).

Define moment of inertia. State its SI unit and dimensions

A stone of mass \(100 g\) attached to a string of length \(50 cm\) is whirled in a vertical circle by giving velocity at lowest point as \(7 m / s\). Find the velocity at the highest point. [Acceleration due to gravity \(=9.8 m / s ^2\) ].

Draw a diagram showing all components of forces acting on a vehicle moving on a curved banked road. Write the necessary equation for maximum safety, speed and state the significance of each term involved in it.

In a conical pendulum, a string of length \(120 cm\) is fixed at rigid support and carries a mass of \(150 g\) at its free end. If the mass is revolved in a horizontal circle of radius \(0.2 m\) around a vertical axis, calculate tension in the string \(\left(g=9.8 m / s ^2\right)\)

Using the energy conservation, derive the expression for minimum speeds at different locations along a al circular motion controlled by gravity.

State an expression for the moment of inertia of a solid uniform disc, rotating about an axis passing through its centre, perpendicular to its plane. Hence derive an expression for the moment of inertia and radius of gyration:
(i) about a tangent in the plane of the disc, and (ii) about a tangent perpendicular to the plane of the disc

Derive an expression for linear velocity at lowest position, midway position and the top-most position for a particle revolving in a vertical circle, if it has to just complete circular motion without string slackening at top.

State and prove the theorem of 'parallel axes'.