3B6 Rotational Motion

Question 1

Define:

rotational motion

Answer 1

Occurs when an object spins around an internal axis rather than moving in a straight line.

Unlike linear motion, which follows a path, rotational motion involves angular displacement, velocity, and acceleration around a fixed point. An example is an ice-skater spinning on a spot of ice.

Question 2

What are the rotational equivalents of acceleration, force, momentum, velocity, and mass?

Answer 2

• Angular acceleration (α)
• Torque (τ)
• Angular momentum (L)
• Angular velocity (ω)
• Moment of inertia (I)

These rotational quantities follow similar principles as their translational counterparts but are adapted to describe motion around an axis.

Question 3

How does Newton’s First Law apply to rotational motion?

Answer 3

An object in rotational motion will continue spinning at a constant angular velocity.

An object at rest will remain at rest unless acted upon by an external, unbalanced torque. This is analogous to the linear case where a body stays in motion unless acted upon by an unbalanced force.

Question 4

What is Newton’s second law of rotation?

Answer 4

Net torque (𝜏) acting on an object is equal to the product of its moment of inertia (I) and angular acceleration (α): 𝜏= Iα.

This law parallels Newton’s second law of motion for linear systems (F=ma) and explains how rotational motion changes under the influence of torque.

Question 5

What is Newton’s third law of rotation?

Answer 5

For every torque exerted by one object on another, there is an equal and opposite torque exerted back on the first object.

This principle underpins interactions in rotational systems, such as the balanced torques observed in static equilibrium or spinning machinery.

Question 6

What is the main difference between translational and rotational motion?

Answer 6

• Translational motion occurs when an object moves along a straight or curved path without rotating.
• Rotational motion occurs when an object spins around an internal axis, either while remaining in place or moving.

Both types of motion follow similar laws.

Question 7

Define:

Angular displacement

Answer 7

The angle through which an object rotates around a fixed axis, measured in radians or degrees.

It is analogous to linear displacement in linear motion.

Question 8

Fill in the blank:

The rate of change of angular displacement over time is called _____ ______.

Answer 8

angular velocity

Angular velocity is measured in radians per second (rad/s).

Question 9

True or False:

Angular displacement is scalar, not vector.

Answer 9

False

Angular displacement is a vector quantity with both magnitude and direction.

Question 10

What is the formula for calculating angular displacement in term of arc length?

Answer 10

Δθ = s/r

Where s is the arc length and r is the radius. Two of the three variables must be known to find the third.

Question 11

Define:

Angular acceleration

Answer 11

The rate at which angular velocity (𝜔) changes over time.
## Footnote

Denoted by α, it describes how quickly an object’s rotational speed increases or decreases and is measured in radians per second squared (rad/s²).

Question 12

Why is angular acceleration important in rotational motion?

Answer 12

Angular acceleration indicates how quickly an object’s rotation rate is changing, influencing its rotational dynamics.

It is measured in radians per second squared (rad/s²).

Question 13

Fill in the blank:

Angular momentum is the rotational equivalent of _____ ______ in linear motion.

Answer 13

linear momentum

It is the product of rotational inertia and angular velocity. Represented as L=I⋅ω.

Question 14

Define:

Torque

Answer 14

Measure of the rotational force acting on an object, causing it to rotate about an axis.

Torque depends on the force applied, the distance from the axis, and the angle of application.

Question 15

How does torque influence rotational motion?

Answer 15

Torque causes changes in an object’s rotational motion, determining the angular acceleration.

It is the rotational equivalent of force in linear motion.

Question 16

True or False:

Angular momentum is always conserved in a system with no external torques.

Answer 16

True

This principle is called the conservation of angular momentum.

Question 17

Fill in the blank:

The resistance of an object to changes in its rotational motion is called ______ _____.

Answer 17

rotational inertia (moment of inertia)

It depends on the mass distribution relative to the axis of rotation.

Question 18

What happens to a spinning skater’s angular velocity when they pull their arms inward, and why?

Answer 18

The angular velocity increases.

By conserving angular momentum, reducing the moment of inertia increases angular velocity.

Question 19

Fill in the blank:

The formula for angular velocity is ω= Δθ/Δt, where ω represents ______ ______.

Answer 19

angular velocity

Δθ is the angular displacement, and Δt is the time interval.

Question 20

How does angular acceleration differ from linear acceleration?

Answer 20

Angular acceleration affects rotation, while linear acceleration affects straight-line motion.

Both measure the rate of change of velocity but in different contexts.

Question 21

Fill in the blank:

The angular displacement of a rotating wheel can be calculated using the formula θ=ωt+(1/2)αt², where α is ______ ________.

Answer 21

angular acceleration

This equation is similar to x=vt+(1/2)at²

Question 22

Fill in the blank:

The angular momentum of a system is conserved if there is no net _______ _____ acting on it.

Answer 22

external torque

This principle applies to both rotational and linear motion.

Question 23

True or False:

Angular momentum can increase without applying torque.

Answer 23

False

Angular momentum changes only when an external torque is applied.

Question 24

How does angular momentum change when an object moves in a larger orbit at a lower speed?

Answer 24

It remains constant due to the conservation of angular momentum.
## Footnote

As the radius increases, the velocity decreases proportionally to keep the total angular momentum unchanged. The larger radius compensates for the lower velocity.

Question 25

Explain why a diver tucks their body during a flip to **spin faster**.

Answer 25

Tucking **reduces the moment of inertia**, increasing angular velocity to conserve angular momentum. ## Footnote This demonstrates the conservation of angular momentum.

Question 26

Why do **tornadoes** spin faster as they become more compact?

Answer 26

As the **radius of the rotating air decreases**, the spinning gets faster. ## Footnote This results in a storm with incredible power.

Question 27

# Fill in the blank: The **moment of inertia** depends on an object’s \_\_\_\_\_ and its distance from the axis of rotation.

Answer 27

mass ## Footnote Greater mass farther from the axis increases the moment of inertia.

Question 28

How does **conservation of angular momentum** affect Earth's rotation?

Answer 28

**Redistribution of mass**, such as melting glaciers, can alter Earth's moment of inertia, slightly changing its rotational speed. ## Footnote This effect is measurable but typically very small.

Question 29

# Fill in the blank: **Torque** depends on the force applied, the distance from the axis, and the \_\_\_\_\_ of application.

Answer 29

angle ## Footnote Maximum torque occurs when the force is perpendicular to the radius.

Question 30

# True or False: A larger **moment of inertia** means an object is harder to rotate.

Answer 30

True ## Footnote Rotational inertia increases with mass and its distribution relative to the axis.

Question 31

A wrench applies a **50 N force** at a **distance of 0.2** m from the axis. What is the **torque**?

Answer 31

𝜏=F⋅r=50N⋅0.2m=10Nm ## Footnote Torque is measured in Newton-meters (Nm).

Question 32

# Define: Static equilibrium

Answer 32

A state where an **object is not rotating**, and the net torque acting on it is zero. ## Footnote This ensures both rotational and translational balance.

Question 33

# Fill in the Blank: For an object to remain in **static equilibrium**, both the **net force** and net \_\_\_\_\_ must equal zero.

Answer 33

torque ## Footnote This ensures no linear or rotational motion occurs.

Question 34

# True or False: An object moving at constant velocity is in **static equilibrium**.

Answer 34

False ## Footnote Static equilibrium means an object is at rest with no net force or torque acting on it. If an object moves at constant velocity, its forces are balanced, but it remains in motion.

Question 35

Why do tightrope walkers use long poles for **balance**?

Answer 35

The pole **increases their moment of inertia**, slowing their rotational motion and allowing more time to regain balance. ## Footnote This reduces the effect of small shifts in center of mass.

Question 36

How is **angular displacement** commonly expressed?

Answer 36

In radians or degrees. ## Footnote 1 radian is equal to 57.3 degrees.

Question 37

What happens to the **angular momentum** of a car's motor when it is turned off?

Answer 37

It is **conserved** as it returns to rest. ## Footnote The car starts with no angular velocity and ends with no angular velocity, conserving angular momentum.

Question 38

# Fill in the blank: A system is in **static equilibrium** if it is at rest and the forces and other factors influencing the object are all \_\_\_\_\_\_.

Answer 38

balanced ## Footnote Linear and angular accelerations must also be zero.