Bridge to university · Sciences
Bridge: physics skills for first-year science
SI units and prefixes, vectors, the constant acceleration equations, free-body diagrams, forces and energy, reviewed before first-year physics.
About this deck
First-year physics usually opens with mechanics, and the opening weeks lean heavily on skills from Grade 11 and 12. This deck reviews them in a compact form: SI units and prefixes, scalars and vectors, resolving and adding vector components, the constant acceleration equations, free fall and projectile motion, Newton's three laws, free-body diagrams with weight, normal force and friction, and work, energy, power and momentum. Several cards are short problems with the numbers worked out so you can compare your method.
The deck is meant for students entering science, engineering, kinesiology or health programs with a physics requirement. Before flipping each card, say which quantities are known and which equation links them; choosing the right equation is often harder than solving it. Draw a free-body diagram every time forces appear, even when the problem seems easy. Common mistakes include mixing up distance and displacement, changing the sign convention halfway through a problem, adding vector magnitudes directly, drawing forces that an object exerts instead of forces acting on it, and forgetting to convert grams to kilograms or kilometres per hour to metres per second.
Before you start: Grade 11 physics, right-triangle trigonometry and rearranging formulas.
All 37 cards
Cover the definitions with a sheet of paper and test yourself, or use the study modes above.
Units
- SI base units
- The seven building-block units: metre, kilogram, second, ampere, kelvin, mole and candela. All others are made from these.Example: Speed in m/s combines metre and second
- Newton (unit)
- The derived unit of force, equal to kg m/s^2: the force that gives 1 kg an acceleration of 1 m/s^2.Example: Lifting a 100 g apple takes about 1 N
- Joule
- The unit of energy and work, equal to one newton acting through one metre (kg m^2/s^2).Example: Lifting 1 N through 1 m
- Watt
- The unit of power: one joule transferred per second.Example: A 60 W bulb uses 60 J each second
- Prefixes kilo, mega, giga
- 10^3, 10^6 and 10^9.Example: 4.2 MJ = 4.2 x 10^6 J
- Prefixes milli, micro, nano
- 10^-3, 10^-6 and 10^-9.Example: 350 nm = 3.50 x 10^-7 m
- Dimensional check
- Confirm both sides of an equation have matching units; a mismatch exposes an algebra slip.Example: If speed comes out in m/s^2, something went wrong
Vectors
- Scalar
- A quantity with size only, such as mass, time, distance, speed or energy.Example: 5 kg
- Vector
- A quantity with both size and direction, such as displacement, velocity, acceleration or force.Example: 12 m/s north
- Resolving into components
- For size A at angle theta from the +x axis: Ax = A cos theta and Ay = A sin theta.Example: 20 N at 30 degrees: about 17.3 N along x and 10.0 N along y
- Magnitude from components
- sqrt(Ax^2 + Ay^2); the direction is arctan(Ay/Ax), adjusted for the quadrant.Example: (3, 4) has size 5
- Adding vectors
- Add all x components, add all y components, then rebuild the resultant. Sizes add directly only when directions match.Example: 3 N east plus 4 N north gives 5 N, not 7 N
- Displacement versus distance
- Change in position, a vector, versus total path length, a scalar.Example: One lap of a 400 m track: path 400 m, change in position 0
- Velocity versus speed
- Rate of change of position including direction, versus how fast regardless of direction.Example: Driving a full loop at 50 km/h: constant speed, changing direction
Kinematics
- v = v0 + a t
- Final velocity after constant acceleration a for time t; use it when displacement is not involved.Example: From rest at 3.0 m/s^2 for 4.0 s: 12 m/s
- d = v0 t + (1/2) a t^2
- Displacement under constant acceleration when the final velocity is unknown.Example: From rest at 2.0 m/s^2 for 5.0 s: 25 m
- v^2 = v0^2 + 2 a d
- Links speeds and displacement without needing time.Example: A car at 20 m/s braking at -5.0 m/s^2 stops in 40 m
- d = ((v0 + v)/2) t
- Displacement equals average velocity times time; valid when acceleration is constant.Example: Speeding up from 10 to 20 m/s over 4.0 s covers 60 m
- Free fall
- Motion under gravity alone. Near Earth the acceleration is about 9.8 m/s^2 downward for every mass, ignoring air.Example: A dropped key and a dropped book land together in a vacuum
- Sign convention
- Pick a positive direction at the start and keep it. If up is positive, g is -9.8 m/s^2 whether the object rises or falls.Example: A ball thrown up has positive velocity and negative acceleration
- Projectile motion
- Horizontal and vertical motions are independent: constant horizontal velocity, constant downward acceleration g.Example: A ball rolled off a table lands at the same time as one dropped beside it
- Ball thrown up at 14.7 m/s: time to the top?
- At the top the vertical velocity is 0, so t = (0 - 14.7)/(-9.8) = 1.5 s.
Forces
- Newton's first law
- An object keeps its velocity, including staying at rest, unless a net external force acts on it.Example: A puck glides on ice until friction slows it
- Newton's second law
- Net force equals mass times acceleration, Fnet = m a, applied separately along each axis.Example: 10 N net on 2.0 kg gives 5.0 m/s^2
- Newton's third law
- Forces come in pairs: if A pushes B, B pushes A equally hard in the opposite direction. The pair acts on different objects.Example: Your feet push the ground back; the ground pushes you forward
- Free-body diagram
- A sketch of one object as a dot with an arrow for every force acting on it, not forces it exerts, used to write Fnet = m a.Example: Book on a table: weight down, normal force up
- Weight
- The gravitational force on a mass, W = m g, measured in newtons. Mass in kilograms is a different quantity.Example: A 60 kg person: about 588 N
- Normal force
- The perpendicular push from a surface. It equals m g only on level ground with no other vertical forces.Example: On a ramp it equals m g cos theta
- Friction
- A force opposing sliding, with a maximum size of mu times the normal force.Example: mu = 0.30 and N = 50 N allow up to 15 N
- Equilibrium
- Net force of zero, so no acceleration: the object is at rest or moving at constant velocity.Example: A lamp hanging still from a cord
- Block on a frictionless 30 degree ramp: acceleration?
- Along the slope, a = g sin 30 = 9.8 x 0.5 = 4.9 m/s^2, the same for any mass.
Energy and momentum
- Kinetic energy
- Energy of motion, equal to (1/2) m v^2.Example: 2.0 kg at 3.0 m/s has 9.0 J
- Gravitational potential energy
- m g h, measured from a reference height you choose.Example: 5.0 kg lifted 2.0 m gains 98 J
- Work
- F d cos theta: force times displacement times the cosine of the angle between them. Zero if nothing moves.Example: Pushing 10 N through 3.0 m in the same direction transfers 30 J
- Conservation of mechanical energy
- With no friction or air resistance, kinetic plus potential energy stays constant.Example: Dropped from 5.0 m: v = sqrt(2 x 9.8 x 5.0), about 9.9 m/s
- Power
- Rate of transferring energy, P = W/t, measured in watts.Example: 600 J in 3.0 s is 200 W
- Momentum
- Mass times velocity, p = m v. This vector is conserved in collisions when no external force acts.Example: 0.15 kg at 40 m/s has 6.0 kg m/s