WorksheetsRotational Dynamics Quiz
Total questions: 22
Worksheet time: 11mins
When we say a solid sphere has a smaller radius of gyration compared to a ring of the same mass and radius, it means:
All mass is concentrated at the center.
Most of the mass is distributed farther from the axis.
The average squared distance of the mass from the axis is smaller.
The object rotates faster regardless of torque.
The radius of gyration is most closely analogous to:
Linear displacement.
Standard deviation in statistics.
Tangential acceleration.
Linear momentum.
A door’s ease of rotation depends more critically on:
The mass of the door alone.
Where the force is applied relative to the hinge.
The density of the door material.
The coefficient of friction at the hinge.
Why does applying force at the edge of a door (far from hinge) make it easier to rotate?
The moment of inertia decreases.
The lever arm is larger, giving higher torque.
The radius of gyration increases.
The force acts parallel to the axis.
Two identical rods: one pivoted at its center, the other pivoted at one end. Which has higher resistance to rotation about its pivot?
Both the same.
Pivoted at the center.
Pivoted at one end.
Cannot be compared without mass.
The parallel axis theorem is practically useful because:
It allows us to compute moments of inertia for axes not passing through the center of mass.
It tells us how to distribute mass to lower torque.
It gives the mass distribution of atoms.
It reduces friction in hinges.
Which of the following is a daily-life example of the perpendicular axis theorem?
The rotation of a bicycle wheel in its plane.
Turning a steering wheel.
Computing bending resistance of a beam cross-section.
Rotating a ceiling fan blade.
Why does a flywheel in an engine store rotational energy efficiently?
Because all mass is near the center.
Because mass is concentrated away from the axis, increasing moment of inertia.
Because it has low angular velocity.
Because it reduces torque.
If you push a door very close to the hinge with the same force as at the edge, what happens?
Torque is the same in both cases.
Torque is smaller near the hinge.
The moment of inertia changes.
The door accelerates equally in both cases.
The radius of gyration conceptually represents:
The effective distance where total mass can be assumed to rotate.
The thickness of the rotating body.
The actual radial distance of all particles.
The speed of rotation.
Why is the radius of gyration important in engineering beam design?
It tells us the strength of material bonds.
It quantifies resistance to bending/rotation.
It reduces weight of beams.
It is only for aesthetic reasons.
A child sits at the center of a rotating merry-go-round and then walks to the edge. What happens to the angular velocity (assuming no external torque)?
Increases.
Decreases.
Remains constant.
Becomes zero.
The concept that makes it easier to balance a long stick vertically on your palm rather than a short stick is most directly related to:
Torque only.
Parallel axis theorem.
Moment of inertia and radius of gyration.
Linear acceleration.
Why do ice skaters spin faster when they pull their arms inward?
Their mass decreases.
Their moment of inertia decreases.
Their torque increases.
Their radius of gyration increases.
The perpendicular axis theorem can only be applied to:
Any 3D rigid body.
Any 2D laminar body.
Only cylindrical bodies.
Only spheres.
A ceiling fan rotates faster at low resistance because:
It has lower moment of inertia.
Torque produced by the motor dominates over inertia.
Its radius of gyration is infinite.
The axis theorem applies directly.
Why does a heavier door not necessarily mean harder to open?
Torque only depends on handle position, not mass.
Moment of inertia depends on both mass and distribution.
The hinge reduces its effective mass.
Heavier doors have smaller lever arms.
In sports like cricket or baseball, players use bats heavier at the end. Why?
To increase radius of gyration and impart more angular momentum.
To reduce torque.
To make the bat easier to swing.
To reduce moment of inertia.
Which of the following correctly explains why thin bicycle tires are harder to balance than thicker ones?
They have lower radius of gyration and thus less rotational stability.
They have higher torque.
Their mass is larger.
Their radius of gyration is infinite.
Engineers calculate the radius of gyration of a building’s cross-section during earthquake design because:
It gives the average mass per floor.
It helps understand resistance against torsional oscillations.
It reduces the cost of materials.
It makes the building lighter.
Which of the following is true about a rotating rigid body
Its centre of rotation is at rest
The centre of rotation is at the centre of mass
All points on the body are moving with the same linear velocity
Every points in the body are moving with the same angular velocity
What does Rotational Inertia depend on?
Mass
Mass Distribution
Both Mass and its Distribution
Neither Mass nor its distribution
