Motion in a Plane — Class 11 Maharashtra HSC Physics revision notes
A 6-page visual revision sheet for Motion in a Plane, written for Class 11 Maharashtra HSC Physics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Motion in a Plane in one look
two axes now, resolve first, then it's two straight lines
Displacement vs path length
Displacement
- a vector, the change in position vector, s = x_2 - x_1
- depends only on where you started and where you finished
- can be zero even after a long journey, as it is for one full circle
Path length
- a scalar, the actual distance covered along the way
- never decreases, and never smaller than the magnitude of the displacement
- for one full circle it is the whole circumference
Velocity and acceleration, average and instantaneous
- average velocity = displacement/time interval, average speed = path length/time interval
- instantaneous velocity, the limit as the interval shrinks to zero: v = dx/dt
- that's the slope of the x-t tangent
- instantaneous speed equals the magnitude of instantaneous velocity: over a vanishing interval, path = displacement
- acceleration a = dv/dt = d^2x/dt^2, the slope of the v-t tangent
- average and instantaneous values coincide for uniform motion, not for non-uniform
Equations of motion for uniform acceleration
- velocity after time t
v = u + at - displacement
s = ut + 1/2at^2 - velocity against displacement
v^2 = u^2 + 2as - from the average velocity
s = u+v/2 t
Page 1 of 6. The full sheet, all 6 pages, opens free in the app.
What this Motion in a Plane sheet covers
- rectilinear motion
- Displacement vs path length
- Displacement
- Path length
- Velocity and acceleration, average and instantaneous
- Equations of motion for uniform acceleration
- velocity after time t
- velocity against displacement
- from the average velocity
- Reading a motion graph
- Free fall
- Adding two velocities
- triangle law: B from the head of A, R closes it
- its size, θ between A and B
- its direction from A
- relative motion
- Relative velocity
- Rain and the umbrella
- Boat and wind problems
- Closest approach of two movers
- separation d, angle φ between the joining line and v_rel
- reached after
- Motion in two dimensions
- position, a vector
- velocity
- acceleration
- size and direction
- equations of motion, vector form
- along x
- along y
- projectile
- Projectile motion, the big idea
- Time, height, range
- time to reach the top
- time of flight
- maximum height
- horizontal range
- trajectory, t eliminated
- Special angles of projection
- Velocity of a projectile at any instant
- horizontal component, fixed
- vertical component
- speed at time t
- direction at time t
- Launched horizontally from a height
- falls for
- lands ahead by
- hits the ground at angle
- Projectile on an incline
- incline at β, launch at θ from the horizontal
- range along the slope
- max range up the incline when
- Angular quantities: θ, ω, α
- angle swept at the centre, cutting an arc s
- angular velocity, rad/s
- angular acceleration, rad/s^2
- linear from angular
- circular motion
- Uniform circular motion
- Why a points at the centre
- Centripetal acceleration and force
- acceleration towards the centre
- in terms of ω
- force needed
- Speeding up on a circle
- tangential part, along v
- centripetal part, to the centre
- total acceleration
- angle β between a and v
- Conical pendulum
- vertical balance
- horizontal, the centripetal part
- period
- frequency
- Symbols and units
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Physics chapter by chapter against your real exam dates and free hours, and when the plan reaches Motion in a Plane the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.