Mech

Question 1

Friction

Answer 1

Opposes motion.
F<=μR
If sliding, then F=μR

Question 2

Toppling

Answer 2

When an object is about to topple, the COM is directly above the lowest point of contact

Question 3

Impulse

Answer 3

J is given by Ft or by mv - mu

Question 4

Newton’s law of impact

Answer 4

Speed of separation/ speed of approach = e

vb-va=e(ua-ub)

Question 5

Oblique impact with a smooth surface

Answer 5

When an object hits a smooth plane there is no impulse parallel to the plane, so velocity in this direction is unchanged.

Question 6

Work done, KE and GPE

Answer 6

W=Fd
KE=1/2 mv^2
GPE = mgh

Question 7

Non constant acceleration

Answer 7

a=dv/dt=v*dv/ds

Work done=S(sa to sb) F ds= S(ta to tb) F~°v~ dt

Question 8

Dot product

Answer 8

(ai + bj)°(xi + yj)=ax + by

Also = |vec1||vec2|cosθ where θ is the angle between the two vectors

Question 9

Time of flight

Answer 9

2Usinα/g

Question 10

Range

Answer 10

U^2sin2α/g

Rmax= U^2/g

Question 11

Trajectory

Answer 11

y=xtanα-gx^2(sec^2(x)/2U^2)

Question 12

Inclined plane

Answer 12

Take SUVAT horizontally and perpendicular to the plane

Question 13

Angular velocity

Answer 13

ω=Δθ/t

Question 14

Velocity in circular motion perpendicular

Answer 14

v=rω

Question 15

Acceleration in a circle

Answer 15

a(transverse)=rω’
a(radial)=-rω^2

Also, all suvat equations have circular counterparts

Question 16

Hooke’s law

Answer 16

T=kx where k is the stiffness, measured in Nm^-1
T=λ/lo x where lo is the natural length and λ is the modulus of elasticity, measured in N. It is the same for any string of the same cross section and material.

Question 17

Elastic potential energy/work done

Answer 17

1/2 kx^2

Question 18

Volumes of revolution

Answer 18

V=S(a to b)πy^2dx

Question 19

Centre of mass for uniform solids

Answer 19

Vxbar= S πy^2x dx

Question 20

Area of plane lamina

Answer 20

S(a to b) y dx

Question 21

Centre of mass of uniform lamina

Answer 21

A(xbar, ybar)=(S(a to b) xy dx, S(a to b) y^2/2 dx)