3B6 Rotational Motion Flashcards
Describe the characteristics and functions of rotational motion.
Define:
rotational motion
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.
What are the rotational equivalents of acceleration, force, momentum, velocity, and mass?
- 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.
How does Newton’s First Law apply to rotational motion?
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.
What is Newton’s second law of rotation?
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.
What is Newton’s third law of rotation?
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.
What is the main difference between translational and rotational motion?
- 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.
Define:
Angular displacement
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.
Fill in the blank:
The rate of change of angular displacement over time is called _____ ______.
angular velocity
Angular velocity is measured in radians per second (rad/s).
True or False:
Angular displacement is scalar, not vector.
False
Angular displacement is a vector quantity with both magnitude and direction.
What is the formula for calculating angular displacement in term of arc length?
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.
Define:
Angular acceleration
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).
Why is angular acceleration important in rotational motion?
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).
Fill in the blank:
Angular momentum is the rotational equivalent of _____ ______ in linear motion.
linear momentum
It is the product of rotational inertia and angular velocity. Represented as L=I⋅ω.
Define:
Torque
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.
How does torque influence rotational motion?
Torque causes changes in an object’s rotational motion, determining the angular acceleration.
It is the rotational equivalent of force in linear motion.
True or False:
Angular momentum is always conserved in a system with no external torques.
True
This principle is called the conservation of angular momentum.
Fill in the blank:
The resistance of an object to changes in its rotational motion is called ______ _____.
rotational inertia (moment of inertia)
It depends on the mass distribution relative to the axis of rotation.
What happens to a spinning skater’s angular velocity when they pull their arms inward, and why?
The angular velocity increases.
By conserving angular momentum, reducing the moment of inertia increases angular velocity.
Fill in the blank:
The formula for angular velocity is ω= Δθ/Δt, where ω represents ______ ______.
angular velocity
Δθ is the angular displacement, and Δt is the time interval.
How does angular acceleration differ from linear acceleration?
Angular acceleration affects rotation, while linear acceleration affects straight-line motion.
Both measure the rate of change of velocity but in different contexts.
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 ______ ________.
angular acceleration
This equation is similar to x=vt+(1/2)at²
Fill in the blank:
The angular momentum of a system is conserved if there is no net _______ _____ acting on it.
external torque
This principle applies to both rotational and linear motion.
True or False:
Angular momentum can increase without applying torque.
False
Angular momentum changes only when an external torque is applied.
How does angular momentum change when an object moves in a larger orbit at a lower speed?
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.
Explain why a diver tucks their body during a flip to spin faster.
Tucking reduces the moment of inertia, increasing angular velocity to conserve angular momentum.
This demonstrates the conservation of angular momentum.
Why do tornadoes spin faster as they become more compact?
As the radius of the rotating air decreases, the spinning gets faster.
This results in a storm with incredible power.
Fill in the blank:
The moment of inertia depends on an object’s _____ and its distance from the axis of rotation.
mass
Greater mass farther from the axis increases the moment of inertia.
How does conservation of angular momentum affect Earth’s rotation?
Redistribution of mass, such as melting glaciers, can alter Earth’s moment of inertia, slightly changing its rotational speed.
This effect is measurable but typically very small.
Fill in the blank:
Torque depends on the force applied, the distance from the axis, and the _____ of application.
angle
Maximum torque occurs when the force is perpendicular to the radius.
True or False:
A larger moment of inertia means an object is harder to rotate.
True
Rotational inertia increases with mass and its distribution relative to the axis.
A wrench applies a 50 N force at a distance of 0.2 m from the axis. What is the torque?
𝜏=F⋅r=50N⋅0.2m=10Nm
Torque is measured in Newton-meters (Nm).
Define:
Static equilibrium
A state where an object is not rotating, and the net torque acting on it is zero.
This ensures both rotational and translational balance.
Fill in the Blank:
For an object to remain in static equilibrium, both the net force and net _____ must equal zero.
torque
This ensures no linear or rotational motion occurs.
True or False:
An object moving at constant velocity is in static equilibrium.
False
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.
Why do tightrope walkers use long poles for balance?
The pole increases their moment of inertia, slowing their rotational motion and allowing more time to regain balance.
This reduces the effect of small shifts in center of mass.
How is angular displacement commonly expressed?
In radians or degrees.
1 radian is equal to 57.3 degrees.
What happens to the angular momentum of a car’s motor when it is turned off?
It is conserved as it returns to rest.
The car starts with no angular velocity and ends with no angular velocity, conserving angular momentum.
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 ______.
balanced
Linear and angular accelerations must also be zero.
