Physics Chapter on Circular Motion

What is the correct direction of the angular velocity and angular acceleration for the ceiling fan blades that are revolving anticlockwise with decreasing speed?

In the context of vertical circular motion for a mass of 1 kg tied to a 1.2 m string, what can be inferred about the maximum speed in relation to the minimum speed of 5 m/s?

Which statement is correct regarding the expressions for the moment of inertia (M.I) of different objects?

If the radius of gyration of a uniform disc about its central and transverse axis is √2.5, what is the radius of gyration about a tangent in its plane?

What is the implication of having a particle tied to a string performing vertical circular motion under gravity?

Exercise - Uniform Circular Motion

Angular velocity indicates the direction of rotation around an axis, while angular acceleration reflects the change in speed or direction of that rotation.
For a ceiling fan rotating anticlockwise with decreasing speed, both angular velocity and angular acceleration point downwards.

Particle in Vertical Circular Motion

A 1 kg particle spins on a 1.2 m string, performing vertical circular motion under gravity.
The minimum speed required for the particle to maintain its circular path is 5 m/s.
Maximum speed for the particle can be estimated as 5√5 m/s.
The difference in tensions in the string between maximum and minimum conditions is calculated to be 60 N.

Moments of Inertia (M.I.)

Different objects have unique formulas for their moments of inertia, essential in understanding rotational dynamics.
The moments of inertia for a hollow right circular cone and a disc are not the same when rotating about their central axes.
For a parallelepiped rotating about an axis passing through its center, its depth influences the expression for its moment of inertia.
The moments of inertia for a rod and a plane sheet differ when calculated about a transverse axis.

Radius of Gyration of a Uniform Disc

The radius of gyration is a metric that represents how mass distribution affects rotational inertia.
For a uniform disc, the radius of gyration about its central and transverse axis is given as √2.5.
The radius of gyration about a tangent in the disc's plane is determined to be 2.5.

This quiz covers key concepts in uniform circular motion, including angular velocity and acceleration, vertical circular motion, and moments of inertia. Test your understanding of how these principles apply to various physical scenarios, such as particles in motion under gravity and the dynamics of rotating objects. Perfect for physics students exploring rotational dynamics.