Rotational Kinematics
A wheel spins at 2 rad/s for 5 s. What is its angular displacement?
10 rad
What is the formula connecting v and ω?
v=rω
Define torque formula.
τ=rFsinθ
What two main factors affect rotational inertia?
Mass & distribution of mass
Condition for rotational equilibrium?
∑τ=0
A disk starts from rest and accelerates at 3 rad/s² for 4 s. What is its angular velocity?
12 rad/s
A point 0.75 m from the center moves at 3 m/s. Find ω.
4 rad/s
10 N force, 0.5 m lever arm, perpendicular. Find torque.
5 Nm
Hoop vs. solid disk (same mass & radius): which has greater I?
Hoop
30 kg child 2 m from pivot. Where should 20 kg child sit for balance?
3 m
A rotating object at 6 rad/s slows down at 2 rad/s². How many radians until it stops?
9 rad
A yo-yo axle radius = 0.02 m. Find acceleration relation.
a=rα
Wrench at 30°: torque formula?
τ=rFsin30°
Moment of inertia of thin rod about center?
(1/12)ML^2
In equilibrium: what about net force & net torque?
Both = 0
A wheel starts from rest, accelerates at 2 rad/s². How long to complete 10 revolutions? (1 rev = 2π rad)
~5.6 s
Rolling sphere: Relation between a and α?
a=rα
General torque formula?
τ=rFsinθ
Hollow or solid sphere faster down incline?
Solid sphere
Uniform beam, two supports: what must forces satisfy?
∑F=0,∑τ=0
Angular acceleration = 5 rad/s². Time for angular velocity to change from 10 rad/s to -10 rad/s?
4 s
For rolling without slipping, velocity of contact point (ground)?
0 m/s
Torque τ(t)=4t Nm. Angular displacement after 2 s?
~8 rad
Moment of inertia rod about one end?
(1/3)ML^2
3 m plank, mass 20 kg, supports 2 m apart. Max distance for 70 kg person before tipping?
~0.71 m