Rotational Kinematics
θ; radians definition...
What is the symbol and unit for angular displacement?
The only thing that linear and rotational motion describe...
What is motion?
Torque is the angular equivalent of...
What is force?
The measure of an object's resistance to changes in its rotational motion; the rotational analog of mass.
What is rotational inertia?
What is the rotational equivalent of Newton’s First Law (an object at rest stays at rest...)?
What is an object at rest or rotating at constant angular velocity will stay that way unless acted on by a net external torque?
Angular velocity is not constant...
What is an ice skater pulling her arms in, or a CD coming to a stop, or a kid pushing a merry-go-round?
(or any other example like that)
The three relationships between rotational and linear motion are equations...
what is
0(theta) = x/r
w = v/r
a(sigma) = a/r
Applying more torque will...
What is an increased angular acceleration?
The net force acting on an object is zero, resulting in constant velocity (either at rest or moving at a constant speed)
What is rotational equilibrium?
What quantity resists changes in rotational motion, just like mass resists changes in linear motion?
What is rotational inertia (moment of inertia)?
Formula for Angular Acceleration
What is a = ^w/^t
The slope of an angular acceleration versus time graph...
What is the area under the curve (change in angular speed)?
A person tries to lift a stone by using a lever. If the lever arm is constant and the mass of the stone increases, what is true of the torque necessary to lift it?
What is the torque increases because the torque is directly proportional to the mass of the body.
What is
Two equal forces pointing in the same direction on opposite sides of the fulcrum
Two equal forces pointing in the opposite direction on the same side of the fulcrum
State Newton’s Second Law in rotational form, relating torque, moment of inertia, and angular acceleration.
What is net torque equals moment of inertia times angular acceleration?
(Or formally: τ = Iα)
A pulley spinning at 40rad/s comes to a stop after spinning through 80 radians. What is the angular acceleration?
What is α=-10rad/s^2?
A disc makes 4 turns in 2 seconds. What is the average angular velocity?
What is ωavg = 4π rad/s?
The torque produced when 12 N of force is applied 1.0 m away from the pivot point, perpendicularly to the lever arm...
What is 12 N?
A solid disk and a hoop, each with the same mass and radius, are released from rest at the top of an identical ramp. Which one reaches the bottom first, and why?
What is the solid disk, because it has a smaller rotational inertia relative to its mass and radius?
A constant net torque is applied to a wheel. What happens to the angular acceleration if the moment of inertia of the wheel doubles?
What is the angular acceleration cut in half?
(Since α = τ / I, if I doubles, α becomes half.)
The four rotational kinematic equations...
ω = ω₀ + αt
θ = ½(ω₀ + ω)t
θ = ω₀ + ½αt²
ω² = ω₀² + 2αθ
A ball spins at 150rad/s and slows down to 100rad/s in 25 seconds. What is the average angular acceleration?
What is -2rad/s^2
A uniform meterstick is balanced at its center on a fulcrum. A 2.0 kg mass is hung at the 20 cm mark. Where should a 3.0 kg mass be hung to keep the meterstick perfectly balanced?
What is at the 47 cm mark?
A beam of length 4 meters and mass 20 kg is supported horizontally by two supports, one at each end. A 60 kg student stands 1 meter from the left end. What is the force exerted by the right support?
What is 450 N?
(Requires setting net torque = 0 and solving for the support forces.)
A disk of radius 0.5 meters and mass 2.0 kg is initially at rest. A constant net torque of 1.0 N·m is applied. What is the angular acceleration of the disk?
(Hint: Moment of inertia for a solid disk = (1/2)MR²)
What is 4 rad/s²?