Vectors and 2D Motion
Why can’t you just add vector lengths to find the resultant?
Because direction matters.
Vectors must be added using angles or components.
What is the acceleration acting on all objects in free fall near Earth?
g=9.8m/s² downward
Define centripetal acceleration.
Acceleration toward the centre of circular motion.
State Newton’s Law of Universal Gravitation.
F=G x (m1m2/r2)
In a circular orbit, what provides the centripetal force?
Gravity.
State the difference between a scalar and a vector quantity?
Scalars have only magnitude (e.g. distance).
Vectors have both magnitude and direction (e.g. displacement, velocity, force).
In projectile motion, which component of motion stays constant (ignoring air resistance)?
Horizontal velocity.
State the formula for centripetal acceleration.
ac=v2/r
What happens to the gravitational force if the distance doubles?
It becomes one-quarter as strong.
State the formula for orbital velocity.
v=/sqrt(GM/r)
If you walk 3 m east, then 4 m north, what is your resultant displacement?
5m at 53°N of E
A ball launched at 20 m/s at 30°—find its initial vertical velocity component.
vy=20sin30°=10m/s
What provides the centripetal force when a car turns a corner?
Friction between tyres and the road.
Write the formula for gravitational field strength g at distance r.
g=GM/r2
What is the relationship given by Kepler’s Third Law?
T2 is proportional to r3
A 10 N force acts at 30° above the horizontal. Find its horizontal component.
10cos30°=8.7N
On an incline of 20°, find the acceleration down the slope (no friction).
a=gsin20°=3.35m/s²
Why does an object moving in a circle experience acceleration even at constant speed?
Its direction (velocity vector) is constantly changing.
In what direction do gravitational field lines point?
Toward the centre of the mass, creating the field.
A satellite orbits Earth every 24 h. What type of orbit is this?
Geostationary orbit.
A boat travels 6 m/s north while a current flows 4 m/s east. What is its resultant velocity and angle?
v=7.2m/s at 34°E of N
A 4 kg block slides down a 25° slope with a=2.5m/s². Find μ.
μ=0.26
A 2 kg mass moves at 4 m/s in a circle of radius 1 m. Find Fc.
Fc=mv2/r=32N
A 5 kg object is 6.4×10⁶ m from Earth’s centre. Find its weight
F=49N
A satellite orbits Earth at a height of 800 km.
Find its orbital speed.
(Mearth=5.97×1024kg, rearth=6.37×106m)
v=7.5×103 m/s