Physics IA1

What are the key assumptions of projectile motion?

• Only gravity acts on the projectile

• Gravity is constant (≈ 9.8 m/s² downward)

• Horizontal motion has constant velocity

• Vertical motion is uniformly accelerated

What equations describe vertical motion in a projectile

• vy=uy+atv_y = u_y + atvy​=uy​+at

• sy=uyt+12at2s_y = u_y t + \frac{1}{2}at^2sy​=uy​t+21​at2

• vy2=uy2+2asyv_y^2 = u_y^2 + 2as_yvy2​=uy2​+2asy​

What are the key projectile formulas for range, flight time and max height?

• R=gu2sin(2θ)​

• t=2usin⁡θgt = \frac{2u\sin\theta}{g}t=g2usinθ​

• H=u2sin⁡2θ2gH = \frac{u^2 \sin^2\theta}{2g}H=2gu2sin2θ​

What is the normal force on an incline

FN​=mgcosθ

What is the component of weight parallel to the incline

F∥​=mgsinθ

What is friction on an incline and the net acceleration with friction

• Ff​=μmgcosθ

• a=gsin⁡θ−μgcos⁡θa = g\sin\theta - \mu g\cos\thetaa=gsinθ−μgcosθ

What is the key logic for inclined planes

• Resolve weight into parallel and perpendicular components

• Object accelerates if mgsin⁡θ>Ffmg\sin\theta > F_fmgsinθ>Ff​

What is centripetal acceleration

ac​=rv2​=ω2r

What is centripetal force (and formula)

Fc​=rmv2​

How are speed, radius and period related

• v=2πrTv = \frac{2\pi r}{T}v=T2πr​

• f=1Tf = \frac{1}{T}f=T1​

What situations fall under horizontal circular motion

• Conical pendulum

• Car on flat/banked curve

• Object whirled in horizontal circle

What are the tension components in a conical pendulum?

• Tcosθ=mg

• Tsin⁡θ=mv2rT\sin\theta = \frac{mv^2}{r}Tsinθ=rmv2​

Useful conical pendulum formulas

• r=Lsin⁡θr = L\sin\thetar=Lsinθ

• v=rgtan⁡θv = \sqrt{rg\tan\theta}v=rgtanθ​

• T=mgcos⁡θT = \frac{mg}{\cos\theta}T=cosθmg​

Key logic for conical pendulums?

• Vertical tension supports weight

• Horizontal tension = centripetal force

• Smaller angle → slower motion

What is the condition for a frictionless banked curve?

tanθ=rgv2​

Speed for a frictionless banked curve?

v=rgtanθ​

Key logic for banked curves?

• Normal force provides centripetal force

• No friction needed

• Speed depends on r,g,θr, g, \thetar,g,θ

Tension at the top of a vertical circle?

T=rmv2​−mg

Minimum speed at the top of a vertical circle?

vmin​=gr​

Tension at the bottom of a vertical circle?

T=mg+rmv2​

Key logic for vertical circles?

• Tension varies with height

• Top: tension smallest

• Bottom: tension largest

• Gravity always acts downward

Max speed over a hill without losing contact?

vmax​=rg​

Normal force or tension at the bottom of a dip?

N=mg+rmv2​

Key logic for hills vs dips?

• Hill → normal smaller

• Dip → normal larger

• Losing contact when N=0N = 0N=0 at hill top

What is gravitational field strength?

g=f/m

Point-mass gravitational field?

g=r2GM​

Law of Universal Gravitation?

F=r2GMm​

How does gravitational field strength change with mass and distance?

• If M increases → g increases

• If r increases → g decreases

What fundamental principle applies to gravitational forces?

Equal and opposite forces (Newton’s Third Law)