PRACTICE COLLECTION / 34 PROBLEMS
Rotation & gravity
Connect torque, rolling motion and orbits. Each problem includes progressive hints, guided reasoning and a question to test the idea again. Problems marked “Free sample” are complete for everyone; membership opens the rest.
A CONNECTED PRACTICE PATH
From an axis choice to a collision
Start by naming the body, the axis and the time interval. Then decide which constraints and conservation laws apply. Revisit the transfer question after closing the worked solution.
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LEARN BEFORE YOU PRACTISE
Build the reasoning first.
Torque, rotational inertia and fixed-axis dynamics
Derive the axis-dependent quantities that connect turning forces to angular motion.
11 worked examples · 11 checks →Rolling motion and angular momentum
Connect the contact constraint to rotation, then choose when angular momentum is the conserved quantity.
10 worked examples · 11 checks →Gravitational fields, orbits and escape
Distinguish vector fields from potential energy and apply the right model inside and outside a sphere.
13 worked examples · 15 checks →CONCEPTS IN THIS COLLECTION
PRACTISE AT YOUR PACE
Problems in this collection
34 problems · Showing 12
Rotation & gravity
Add moments about intersecting axes
Find its moment of inertia about the normal axis through the center.
Apply a principleRotation & gravity
A couple changes the support share
What is the upward reaction at the right support?
Connect conceptsRotation & gravity
Infer the mass distribution from a descent
What value of β follows from the energy measurements?
Find a missing quantityRotation & gravity
A torque graph can reverse a rotor
What is its angular velocity at t=4 s?
Read graphs & measurementsRotation & gravity
Undo the old axis shift first
What is the new moment of inertia?
Find a missing quantityRotation & gravity
Two distances describe one ellipse
What is its orbital eccentricity?
Read graphs & measurementsRotation & gravity
Subtract the surface after finding the orbit
What is its altitude above the surface?
Apply a principleRotation & gravity
Connect angular rate, acceleration and displacement
Through what angle does it turn before its angular velocity doubles?
Connect conceptsRotation & gravity
Signed angular momentum survives internal friction
What is their common final angular velocity?
Apply a principleRotation & gravity
Weights locate the gravity resultant
Where must one upward support force act to balance both force and torque?
Compare casesRotation & gravity
Use the mass inside the point
Find the gravitational field magnitude at distance R/4 from its center.
Compare casesRotation & gravity
An equivalent radius for a rod
Find its radius of gyration about an axis perpendicular to the rod through one end.
Connect concepts12 of 34 shown