Ƭ = Iα
What is the relationship between torque and rotational inertia.
y = A Sin ωt
What's the relationship between displacement in SHM and time ?
ac = v2 /r
What's the formula for centripetal acceleration ?
D = (m1d1 + m2d2) / (m1 + m2)
What's the formula for the position of the CM between two bodies ?
Ek = 1/2 Iω2
What's the formula for rotational kinetic energy ?
Ɵ = ω t
What's the formula for angular displacement as a function of time and angular velocity ?
a = - ω2 y
What's the formula definition of SHM ?
Fc = N Sin Ɵ
What's the relationship between the centripetal force , normal force and angle for banked corner motion ?
ΡT = (m1 + m2) Vcm
What's the relationship between total momentum, velocity of CM and masses ?
mg = T Cos Ɵ
What's the relationship between the weight of the bob, tension and angle for conical pendulum ?
The sum of products of mass increments times square of distance from rotational axis
What's the definition of rotational inertia ?
velocity is a maximum and acceleration is a minimum and changing in direction
What is happening to velocity and acceleration in SHM at equilibrium point ?
R = GM/ v2
How does the radius of satellite motion vary with linear speed, and mass of orbited body ?
The system is closed
What's the assumption for conservation of momentum ?
The restoring force is the component of the weight force in the direction of the equilibrium point
What provides the restoring force for pendulum SHM ?
cylinder > solid sphere
Compare the rotational inertias of cylinder and solid sphere
Draw graph of displacement versus time for damped oscillations
T = 2πsqrt(r^3/(GM)
What's the formula for the period of satellite orbit as function of orbit radius and mass of orbitted body ?
eg Describe the path of CM for a diver
The satellite moves to a higher orbit
What happens if a satellite speeds up ?
or What happens if a satellite gains energy ?
It takes longer as its rotational inertia is greater and a greater proportion of rotational kinetic energy is generated at the expense of linear kinetic energy
Why does a cylinder (eg) take longer to roll down a ramp compared to a sphere (eg) ?
When external energy is input at the same frequency as that of the natural frequency of an oscillating system
What is resonance ?
Parabolic motion instead of circular motion
What occurs in vertical circular motion when the weight exceeds the centripetal force (or the speed is less than that required for circular motion) ?
the moving car had angular momentum relative to the stationary one even though the motion was linear
How does a car travelling linearly cause rotation during a collision (with a stationary car) ?
The centre of mass
(suitable definition)