DoAssignment.ca

B2.1 · Use terminology for frames, components, friction, and circular motion

Learn to use terminology for frames, components, friction, and circular motion through clear examples and targeted practice.

Ontario Grade 12 Physics

Dynamics

Frames, vector components, friction, and circular motion | SPH4U B2.1

This lesson builds on SPH3U ideas: motion describes changes in position, and forces can change an object's motion. A scalar has magnitude only, such as time or speed. A vector has magnitude and direction, such as displacement, velocity, or force. Before describing motion, identify the physical system, the reference frame used to observe it, and the positive direction on the chosen coordinate axis. These choices make descriptions clear and consistent. The focus here is the terminology named in expectation B2.1.

What you will learn

Define a physical system, reference frame, coordinate direction, and frame of reference.
Distinguish vectors from scalars and describe vector components.
Use accurate terms for static and kinetic friction.
Describe uniform circular motion using radius, period, frequency, speed, and centripetal acceleration.

1. System, frame, and direction

A physical system is the object or group of objects being studied. For a motion description, the system might be a cyclist, a ball, or a cart. State what belongs to the system so it is clear whose motion or forces are being described.

A reference frame is the viewpoint and coordinate system used to describe position and motion. A frame of reference includes an origin, or zero position, and chosen directions. For example, a person standing beside a road could use the road as the frame and choose forward as positive. A passenger on a moving bus could instead describe motion relative to the bus.

Position and velocity are described relative to a frame. An object can be at rest relative to one frame and moving relative to another. For example, a seated passenger is at rest relative to the bus but moves relative to the road. Neither description is contradictory; each names a different frame.

A coordinate direction is the direction assigned a positive sign. In one-dimensional motion, choose positive before using signs in calculations. A negative velocity then means motion opposite to the chosen positive direction; it does not mean the object is slowing down. Whether an object is speeding up depends on how its velocity and acceleration directions compare.

A component is the part of a vector along one chosen axis. Components are signed quantities. In two dimensions, a vector can be described by horizontal and vertical components. The components together specify the original vector; they are not separate forces unless a physical force acts in each direction.

v_x = v\cos\theta,\quad v_y = v\sin\theta

Name the system, frame, and positive direction before describing motion.
Vectors have magnitude and direction; scalars have magnitude only.
A component is a signed part of a vector along an axis.

2. Components and friction terminology

For a vector with magnitude

v

at angle

\theta

measured from the positive horizontal axis, its horizontal component is

v_x

and its vertical component is

v_y

. The signs depend on the direction of each component. If the vector points up and right, both components are positive under the usual right-and-up convention. If it points down and left, both are negative.

The same component idea applies to forces. A force is a vector, so describing its components can show how much of it acts along each chosen axis. Components help organize a situation; they do not change the actual force.

Friction is a contact force that acts between surfaces touching one another. It acts parallel to the surfaces and opposes sliding or the tendency for sliding at the contact. The direction is therefore set by the relative motion, or possible motion, of the surfaces—not automatically by the object's overall direction of travel.

Static friction applies when the surfaces do not slide relative to each other. It can adjust in size to prevent slipping, up to a maximum value. Kinetic friction applies when the surfaces slide relative to each other. In a simple model, its size is represented by the coefficient of kinetic friction multiplied by the normal force. The normal force is the contact force perpendicular to the surface. A coefficient of friction is a ratio and has no units.

A free-body diagram is a drawing of the forces acting on one selected system. Draw only forces exerted on that system. If a box slides to the right over a level floor, the kinetic friction force on the box points left. If the box is not sliding but is about to slip right, static friction points left. Naming the type and direction prevents confusing friction with the object's velocity.

f_k = \mu_k F_N

Components are signed projections along chosen axes.
Static friction prevents relative sliding; kinetic friction acts during sliding.
Friction is parallel to the contact surface and opposes relative sliding or its tendency.

3. Circular-motion vocabulary

Circular motion occurs when an object follows a circular path. The radius,

r

, is the distance from the centre of the circle to the path. One complete trip around the circle is one revolution. The period,

T

, is the time for one revolution, measured in seconds. Frequency,

f

, is the number of revolutions per second, measured in hertz.

In uniform circular motion, the object's speed stays constant, but its velocity changes because the direction of travel continually changes. Speed is a scalar; velocity is a vector. At any point on the circle, the instantaneous velocity points tangent to the circular path.

The acceleration in uniform circular motion points toward the centre of the circle. It is called centripetal acceleration. The word centripetal means centre-directed. This acceleration describes the change in velocity's direction; it does not mean that the object's speed must be increasing. The net force must also point inward for this circular motion, but the name centripetal refers to the direction and role of the net force, not to a separate kind of force.

A useful way to picture the directions is to draw a circle, mark the centre and the object's position, then draw velocity tangent to the path and centripetal acceleration toward the centre. Keep the system and frame explicit. For a ball moving in a circle on a horizontal surface, for example, describe the ball's motion relative to the surface or room and identify the circle's centre.

f = \frac{1}{T},\quad a_c = \frac{v^2}{r}

Period is time per revolution; frequency is revolutions per second.
In uniform circular motion, speed is constant while velocity changes direction.
Velocity is tangent to the path; centripetal acceleration points toward the centre.

4. Choosing precise language

A good physics description uses words that match the model. Say which frame is being used, rather than simply saying that an object is moving. Say which axis a component belongs to and state its sign convention. For friction, state whether the surfaces slide and identify the direction of relative sliding or possible sliding.

For circular motion, distinguish speed from velocity and state whether the motion is uniform. If the speed is constant, do not describe the velocity as constant: its direction changes. Likewise, centripetal acceleration points inward even when the object is moving around the circle at constant speed.

Use SI units when a quantity has units. Position and radius are measured in metres, time and period in seconds, speed in metres per second, and acceleration in metres per second squared. Direction words or vector notation are needed to complete a vector description.

Use signs only after setting a coordinate direction.
Do not confuse a force's direction with an object's direction of travel.
A complete vector description includes magnitude and direction.

Circular-motion directions and quantities

Quantity	Meaning	Direction or SI unit
Radius	Centre-to-path distance	m
Period	Time for one revolution	s
Frequency	Revolutions per second	Hz
Velocity	Rate and direction of motion	Tangent to path; m/s
Centripetal acceleration	Acceleration for the changing velocity direction	Toward centre; m/s²

Worked example

Resolve a velocity into components

A cart moves at

10.0\ \mathrm{m/s}

30.0^\circ

above the positive horizontal direction. Find its horizontal and vertical velocity components.

Set the frame and axes
The system is the cart, and the frame is the floor beside the track. Choose right as positive horizontal and up as positive vertical. The given velocity points up and right, so both components should be positive.
Use the component relationships
The angle is measured from the positive horizontal axis. The horizontal component uses cosine, and the vertical component uses sine.
$v_x=v\cos\theta,\quad v_y=v\sin\theta$
Substitute and calculate
Use the given speed and angle. Retain metres per second for each component.
$v_x=(10.0\ \mathrm{m/s})\cos(30.0^\circ)=8.66\ \mathrm{m/s},\quad v_y=(10.0\ \mathrm{m/s})\sin(30.0^\circ)=5.00\ \mathrm{m/s}$

Answer: The horizontal component is

8.66\ \mathrm{m/s}

to the right, and the vertical component is

5.00\ \mathrm{m/s}

upward.

Check: Each component has units of velocity. Both are positive, matching the stated up-and-right direction. Their combined magnitude is approximately

10.0\ \mathrm{m/s}

, consistent with the given velocity.

Worked example

Identify friction direction and type

A crate slides to the right across a level floor. Describe the friction force on the crate. Then state the friction type if the crate instead remains at rest while a horizontal push tends to move it right.

Define the system and direction
The system is the crate, viewed from the floor. Choose right as positive. Friction is a contact force parallel to the floor.
Apply the friction terminology
In the first situation, the crate slides relative to the floor, so the friction is kinetic and points left, opposite the relative sliding. In the second situation, the surfaces do not slide. Static friction prevents the crate from starting to slip right, so it points left.

Answer: While the crate slides right, kinetic friction on it points left. While it remains at rest as the push tends to move it right, static friction points left.

Check: The force directions oppose relative sliding or the tendency for relative sliding. The crate's rightward motion in the first case does not make friction point right.

Worked example

Describe a circular path quantitatively

A toy moves at a constant speed of

4.00\ \mathrm{m/s}

around a circle of radius

2.00\ \mathrm{m}

. Find its centripetal acceleration and state its direction.

Define the motion
The system is the toy, described relative to the room. The circle's centre defines the inward direction. The speed is constant, so this is uniform circular motion.
Use the circular-motion relationship
Centripetal acceleration depends on speed squared divided by radius. Its direction is toward the centre of the circle.
$a_c=\frac{v^2}{r}$
Substitute with SI units
Use speed in metres per second and radius in metres. The resulting acceleration unit is metres per second squared.
$a_c=\frac{(4.00\ \mathrm{m/s})^2}{2.00\ \mathrm{m}}=8.00\ \mathrm{m/s^2}$

Answer: The centripetal acceleration is

8.00\ \mathrm{m/s^2}

toward the centre of the circle.

Check: The units reduce to

\mathrm{m/s^2}

. The direction is inward, as required for circular motion. A smaller radius at the same speed would require greater centripetal acceleration.

Common mistakes and how to avoid them

Calling a negative velocity a slowing velocity.

Correction: A negative sign identifies direction relative to the chosen positive axis. Compare velocity and acceleration directions to decide whether speed changes.

Assuming friction always points opposite the object's overall motion.

Correction: Friction opposes relative sliding, or the tendency for sliding, at the contact surface.

Saying velocity is constant in uniform circular motion.

Correction: The speed is constant, but velocity changes because its direction changes.

Treating centripetal force as an additional, separate force.

Correction: Centripetal describes the inward direction of the net force needed for circular motion. Identify the actual forces acting on the system.

Lesson summary

State the system, reference frame, and positive direction before describing motion.
Vectors have magnitude and direction; components describe them along selected axes.
Static friction prevents relative sliding, while kinetic friction acts during sliding.
Uniform circular motion has constant speed, tangent velocity, and inward centripetal acceleration.

Check your understanding

Question 1

A person sits still on a moving bus. Which statement is accurate?

The person is at rest relative to the bus and moving relative to the road.
The person is moving relative to the bus and at rest relative to the road.
The person is at rest in every reference frame.
The person has no position because the bus is moving.

Show answer and explanation

The person is at rest relative to the bus and moving relative to the road.

Motion is described relative to a frame. The person is stationary relative to the bus but moves along with it relative to the road.

Question 2

A puck slides left across a level surface. What is the direction and type of friction on the puck?

Left, kinetic friction
Right, kinetic friction
Left, static friction
Up, kinetic friction

Show answer and explanation

Right, kinetic friction

The puck slides relative to the surface, so friction is kinetic. It acts opposite the relative sliding, to the right.

Question 3

In uniform circular motion, which description is correct?

Velocity is constant and acceleration is zero.
Speed changes while velocity direction stays fixed.
Speed is constant, velocity is tangent, and centripetal acceleration points inward.
Centripetal acceleration points along the tangent.

Show answer and explanation

Speed is constant, velocity is tangent, and centripetal acceleration points inward.

Uniform circular motion has constant speed, but the direction of velocity changes. The velocity is tangent to the circle, and centripetal acceleration points toward its centre.

Key terms

Physical system: The object or group of objects selected for study.
Reference frame: The viewpoint and coordinate system used to describe position and motion.
Component: The signed part of a vector along a selected axis.
Static friction: Friction between surfaces that are not sliding relative to each other.
Kinetic friction: Friction between surfaces sliding relative to each other.
Period: The time required for one complete revolution.
Frequency: The number of complete revolutions per second.
Centripetal acceleration: Acceleration directed toward the centre of a circular path.

Continue through SPH4U

View the complete SPH4U Ontario Grade 12 Physics curriculum and lessons

About this lesson and its review

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 12 Physics (SPH4U), expectation B2.1. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

Official curriculum reference

Report a correction or ask a question