Systems of Particles & Linear Momentum

All maintain equal speeds regardless altitude differences

Higher altitude one due reduced gravitational influence facilitating quicker travel

Lower altitude satellite maintains highest orbital speed

They vary unpredictably because other factors like solar radiation pressure space debris impact more than weightlessness factor alone

Tangential and normal components both become zero as the ball stops completely for an instant.

Normal component reverses direction while tangential acceleration remains constant due to inertia effects.

Both tangential and normal accelerations increase uniformly until the ball ceases to move upwards on the incline plane.

The tangential component becomes zero while normal component remains unchanged due to gravity's consistent effect perpendicular to plane's surface.

The point at which the total mass of the system can be considered to be concentrated

The location where all forces acting on a system are applied

The point at which gravitational force can be considered to act on an object

The balance point where the net torque about any axis is zero

Three quarters distance bottom edge

Centre rectangle

Half way along diagonal

One quarter distance top edge

Trigonometric substitution.

Geometric approximation.

Algebraic manipulation.

Calculus differentiation.

At point (a/3, a/3)

At point (a/2, a/2)

At point (0,a)

At point (a,0)

Roll differently weighted but similar-shaped objects down adjacent slopes coated with varying friction materials noting final speeds only.

Swing diverse objects hanging from strings in pendulum fashion assessing swing duration not accounting shape-induced air resistance effects.

Drop various shaped objects from different heights onto a soft surface recording indent depth as proxy for center-of-mass impact point.

Roll objects with identical masses but different shapes down an incline, timing each descent while confirming no slippage occurs.

It oscillates about a new equilibrium position set by external influences on rotational dynamics.

It remains stationary because only internal forces change relative positions within a system without influencing its overall motion.

It shifts away from applied force as reaction forces within system components adjust their positions.

It moves toward the direction of force application due to rotation causing displacement.

He begins to move outward across the ice owing to centrifugal effects from his initial rotation, creating a horizontal net force.

His rotational speed increases due to conservation of angular momentum leading to a decrease in his moment of inertia.

His spin diminishes as the distribution of mass moves away from the axis of rotation, creating more air resistance against spin.

His rotational speed remains constant as the change in shape has no impact on overall motion without external forces.

Differentiate the acceleration function twice.

Take the derivative of the velocity function.

Find the area under the acceleration-time graph.

Integrate the acceleration function twice.