Kinematics
An object rolls along the floor at a constant angular velocity. A scientist measures its distance (x1) after some time, and again (x2) after twice as much time. How much larger is x2 than x1? (Twice, four times, half)
Twice
An engineer notices that a flywheel with a moment of inertia of 40 kgm2 is too susceptible to outside forces changing its angular velocity. They want to make forces effect its angular velocity half as much.
What should the new angular velocity be?
80 kgm2
A mechanic uses a 1 m wrench to loosen a bolt. If she wants to double the torque she can apply, how long should her new wrench be?
This force is acting as a torque on a wheel placed on a hill.
What is gravity
Angular Velocity
A wheel rolls along the floor at π/2 rad/s. How long will the wheel take to roll one complete revolution?
θ = w * t
t = θ/w
t = (2π rad) / (π/2 rad/s)
t = 4 seconds
Two Objects are acted on by the same torque. Object A rotates at π rad/s2 and object B rotates at π/2 rad/s2. Which object has a greater moment of inertia?
Object B
Two objects have the same moment of inertia and are acted on by different torques. Object A rolls at π rad/s2, and Object B rolls at π/2 rad/s2. Which object is being acted on by a greater torque?
Object A
ϕ, the angle between the radius of a wheel and the force of gravity is equal to what other angle while on a ramp or hill?
The Slope of the hill
This is the rate at which an objects angular velocity changes.
What is Angular Acceleration?
Time
Angle
Angular Velocity
Angular Acceleration
A contestant on a game show spins a wheel with a torque of 4π Nm, the wheel then spins at π/2 rad/s2 as they push.
What is the moment of inertia of the wheel?
8kgm2
a 21 Nm torque is applied to a 3 m lever. Assuming the torque is applied perpendicular (π/2 rad) to the lever, how much force must be applied?
7 N
Two Cylinders with the same mass (2 kg) roll down a hill. One has a radius of 1 m and the other has a radius of 0.5 m. Which wheel does gravity apply a greater torque to?
The 1 m cylinder
This is the name for a force that causes an angular acceleration.
What is Torque?
An object rolls along a ramp at a constant angular acceleration. A scientist measures its distance (x1) after some time, and again (x2) after twice as much time. How much larger is x2 than x1? (Twice, four times, half)
Four times
A wheel is remade with the same shape, same mass, but twice the radius. how does its moment of inertia change? (doubled, quadrupled, halved, stays the same)
Quadrupled
A motor applies a 7 Nm clockwise torque to a lever, and its payload applies a 3 Nm counterclockwise torque. What is the Net Torque on the lever
4 Nm clockwise
A sphere and a cylinder with the same mass and radius roll down a hill. Which should have a greater angular acceleration?
Sphere
This is the measure of an angle Physicists use. Based on half the diameter of a circle
What is a radian (rad)?
A wheel at rest starts to move with an angular acceleration of π/5 rad/s2. How fast will it be rolling at 10 seconds?
w = w0 + a*t
w = 0 + π/5 * 10
w = 2π rad/s
Between a Hoop, a Sphere, and a cylinder, of the same mass and radius, this shape would have the greatest moment of inertia.
What is a hoop?
A 5 N force is applied to a 2 m lever at a π/6 rad angle. How much torque is applied?
5 Nm
Double Jeopardy!
A 2 kg bowling ball with a radius of 0.25 m rolls down a hill on earth with a slope of π/6 radians. Find the Angular Acceleration of the ball as it rolls down the hill.
49 rad/s2
This is the measure of how hard it is to give an object an angular acceleration (its tendency to keep its angular velocity)
What is Moment of Inertia?