AQA M1 Essentials revision PDF

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M1 Essentials: Summary of AQA Mechanics 1 content not provided in the formula book Mechanics terminology Particle Rigid Body Mass, but no size Mass and size, does not deform Rough/Smooth Elastic/Inelastic Friction present/not Deforms/does not deform Light Plane No mass Flat surface (eg, a slope)

Vector Displacement Velocity Acceleration Force N/A N/A

Vectors & scalars Scalar Distance (𝑚) Speed (𝑚𝑠 −1 ) (Magnitude of) acceleration (𝑚𝑠 −2 ) (Magnitude of) force (𝑁) Mass (𝑘𝑔) Time (𝑠)

Graphs of motion Displacement-Time Velocity-Time 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝐻𝑒𝑖𝑔ℎ𝑡 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝐴𝑟𝑒𝑎 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝐻𝑒𝑖𝑔ℎ𝑡 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 SUVAT equations (constant acceleration equations) 𝑣 = 𝑢 + 𝑎𝑡 𝑠 = 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 (𝑚) 𝑣 2 = 𝑢2 + 2𝑎𝑠 −1 𝑢 = 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑚𝑠 ) 𝑢+𝑣 𝑣 = 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑚𝑠 −1 ) 𝑠= 𝑡 2 −2 𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (𝑚𝑠 ) 1 2 𝑠 = 𝑢𝑡 + 𝑎𝑡 𝑡 = 𝑡𝑖𝑚𝑒 (𝑠) 2

𝑎 𝑐 𝑎±𝑐 [ ]±[ ]= [ ] 𝑑 𝑏 𝑏±𝑑

Manipulating vectors 𝑎 𝑘𝑎 𝑘 [ 𝑏] = [ ] 𝑘𝑏

𝑎 |[ ]| = √𝑎2 + 𝑏 2 𝑏

Resolving a vector Eg. A force 𝐹 acting at 𝜃° to the horizontal: 𝐹 cos 𝜃] 𝐹 cos 𝜃 horizontally, 𝐹 sin 𝜃 vertically: 𝑭 = [ 𝐹 sin 𝜃 Kinematics in 2 dimensions Displacement, velocity and acceleration are all vector quantities. In 1 dimensional problems, direction is given as +𝑣𝑒 or −𝑣𝑒. In 2 dimensional problems, direction is defined by the vector. Equilibrium A particle in equilibrium has constant velocity (could be at rest), and has a resultant force of 0𝑁 acting on it (forces are balanced). Friction Friction always acts in the opposite direction to motion or potential motion. Always true In motion, or in limiting equilibrium 𝐹𝑟 ≤ 𝜇𝑅 𝐹𝑟 = 𝜇𝑅 Newton’s second law 𝐹: 𝑟𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑓𝑜𝑟𝑐𝑒 (𝑁) 𝐹 = 𝑚𝑎 𝑚: 𝑚𝑎𝑠𝑠 (𝑘𝑔) 𝑎: 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 (𝑚𝑠 −2 )

Projectiles Horizontal: Vertical: 𝑣 constant 𝑎 = −9.8 𝑥 𝑆𝑈𝑉𝐴𝑇 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 𝑣= 𝑡

Momentum Conservation of momentum: 𝑚1 𝑢 + 𝑚2 𝑢 = 𝑚1 𝑣 + 𝑚2 𝑣...