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24 exam-style questions with model answers, plus 24 quick multi-choice questions — every question on the site for this standard, grouped by the 8 pages of notes they come from.
Write a full answer before you reveal the model one — that comparison is where the marks come from. Every block links back to the notes that teach it.
Two masses lie on a line: kg at and kg at m.
Show that the centre of mass is at m.
A kg mass at m and a kg mass at m sit on a rod.
Calculate the position of the centre of mass.
An astronaut ( kg) and a tool bag ( kg) float at rest in deep space, m apart. The astronaut pulls the bag in until they meet.
Explain where they meet, and why, using the centre of mass.
A kg ball moving east at m s−1 is struck and moves north at m s−1.
Show that the magnitude of its change in momentum is kg m s−1.
A kg trolley moving east at m s−1 collides with a stationary kg trolley and they stick together.
Calculate their common speed.
A kg object at rest explodes into two pieces. A kg piece flies east at m s−1.
Determine the velocity of the kg piece, and explain why kinetic energy is not conserved here.
A kg ball on a string moves in a horizontal circle of radius m at m s−1.
Show that the centripetal force is N.
A car of mass kg rounds a flat (unbanked) corner of radius m at m s−1.
Calculate the friction force needed, and state what provides the centripetal force.
A bucket of water of mass kg is swung in a vertical circle of radius m.
Determine the minimum speed at the top for the water to stay in the bucket, and explain what happens to the normal (contact) force at that speed.
Two kg masses are m apart (centre to centre).
Show that the gravitational force between them is about N. ( N m2 kg−2.)
A satellite orbits a planet of mass kg at a radius of m.
Calculate its orbital speed. ( N m2 kg−2.)
Explain why a geostationary satellite must orbit at one particular radius, and why it can only sit above the equator.
A disc spins at a constant rad s−1.
Show that a point on the rim, m from the axis, moves at m s−1.
A turntable slows from rad s−1 to rest in s at constant angular acceleration.
Calculate the angle it turns through while stopping.
A wheel of radius m accelerates uniformly from rest to rad s−1 in s.
Determine the tangential and centripetal accelerations of a point on the rim at the final instant, and explain why they point in different directions.
A flywheel of rotational inertia kg m2 experiences a net torque of N m.
Show that its angular acceleration is rad s−2.
A disc of rotational inertia kg m2 spins at rad s−1.
Calculate its rotational kinetic energy and its angular momentum.
A student stands on a freely rotating stool holding masses out at arm's length, turning at rad s−1 with rotational inertia kg m2. They pull the masses in, reducing the inertia to kg m2.
Determine the new angular velocity, and explain what happens to the rotational kinetic energy and where any change comes from.
An object in SHM has amplitude m and angular frequency rad s−1.
Show that its maximum speed is m s−1.
An object oscillates in SHM with a period of s and amplitude m.
Calculate its maximum acceleration.
An object in SHM has amplitude m and angular frequency rad s−1.
Determine its speed when it is m from the centre, and explain why the acceleration there is exactly half its maximum value.
A kg mass on a spring of constant N m−1 oscillates in SHM.
Show that its period is about s.
A pendulum has length m. Take m s−2.
Calculate its period, and state what would happen to the period if a heavier bob were used.
Soldiers are told to break step when crossing a footbridge.
Explain, using natural frequency, resonance and damping, why marching in step could be dangerous.