CIRCULAR MOTION
FC = mv2/r
What is the formula for centripetal force ?
y = A sin ω t
What is the formula for displacement over time for SHM ?
Ʃmr2
What is the formula for rotational inertia ?
Ep = 1/2 kx2
What is the formula for the energy stored in a spring ?
ρT = mTvcm
Formula for total momentum related to velocity of CM
Fc = horizontal component of normal contact force ?
For banked corner what force provides centripetal force ?
periodic motion in which the acceleration is proportional to displacement and opposite in motion
What is SHM ?
Ƭ = Iα
What's the relationship between torque and rotational inertia and rot acceleration ?
Ek = 1/2 Iω2
What is the formula for rotational kinetic energy ?
provided there is no external force
When is momentum conserved ?
Nv = Fg
Condition for balanced horizontal motion for banking on a corner
At the centre (equilibrium position) of the SHM motion
Where in SHM is a = 0 (OR speed a max.)
Because a sphere has the lowest rotational inertia
Why does a sphere roll faster down a slope than other round objects ?
damping
What is the name of the process of reducing amplitude of oscillation due to energy losses ?
L = mvr
What is the formula for angular momentum of aan object moving linearly ?
vmin = SQRT(gr)
What's the minimum speed required to complete a vertical circle ?
a = - ω2 y
What's the formula definition of SHM ?
Provided there is no external torque
When is angular momentum conserved ?
Resonance
What happens when a driving frequency is equal to the natural frequency of oscillation of a system maximising amplitude
L = ρr
Relationship between angular and linear momentum ?
v = SQRT (GM/r)
The speed required for a stable orbit of a satellite ?
A ω2
What's the max. acc. in SHM
Because the ice-skater lowers their rotational inertia by bringing their arms and legs in,l conserving angular momentum
How is an ice-skater able to rotate faster without added energy ?
A body rolling down a ramp converts gravitational energy to variable linear and rotational kinetic energy depending on shape
Why do some objects roll faster down a ramp than others ?
the force is minimised by extending the time of the interaction
How to minimise the force (damage) in a collision ?