Exercise \(\PageIndex{1}\): Determine angular displacement
A child sits on a merry-go-round at the position marked by the red circle (position is given in meters and time is given in seconds). What is her angular displacement in radians after \(0.44\) seconds? Restart.
Exercise \(\PageIndex{2}\): Determine angular and tangential speeds and velocity
A child sits on a merry-go-round at the position marked by the red circle (position is given in meters and time is given in seconds). Restart.
- What is her average speed and instantaneous velocity?
- What is her angular speed and angular velocity?
For the instantaneous velocity and angular velocity, you should give a value for the speed and a description of the velocity's direction for any point in time.
Exercise \(\PageIndex{3}\): A quarter and a penny are on a turntable
A quarter and a penny are on a turntable as shown in the animation (position is given in centimeters and time is given in seconds). Restart.
- Which coin has the greater angular speed?
- What are their angular speeds?
Exercise \(\PageIndex{4}\): Determine angular acceleration
A child sits on a merry-go-round at the position marked by the red circle (position is given in meters and time is given in seconds). What is her angular acceleration? Restart.
Exercise \(\PageIndex{5}\): Determine tangential acceleration
A boy sits on a merry-go-round at the position marked by the red circle. A girl gives the merry-go-round a constant tangential push for \(0.2\) seconds as shown in the animation (position is given in meters and time is given in seconds). What is the magnitude of the tangential acceleration of the boy while the girl is pushing the merry-go-round? Restart.
Exercise \(\PageIndex{6}\): Determine angular acceleration of the wheel
A grinding wheel is rotating at constant speed when an object makes contact with the outer edge as shown in the animation (position is given in meters and time is given in seconds). Friction causes the wheel to stop. What is the angular acceleration of the wheel? Restart.
Exercise \(\PageIndex{7}\): What is the average torque on the turntable?
A turntable (a flat disk) of mass \(5.0\text{ kg}\) is rotating at a constant speed when your finger makes contact with the outer edge, as shown in the animation (position is given in meters and time is given in seconds). Friction between your finger and the turntable causes the turntable to stop. What is the average torque on the turntable caused by the frictional force? Restart.
Exercise \(\PageIndex{8}\): Which vector represents the acceleration of the object?
A car starts from rest and accelerates until it is halfway around a circular track. After that time it moves at constant speed (position is given in meters and time is given in seconds). Which animation correctly shows the acceleration vector? Restart.
Exercise \(\PageIndex{9}\): What is the ratio of the kinetic energy?
The animation depicts an idealized drive train for a bicycle. A large green disk (i.e., a flat cylinder) is used to rotate a small green disk of the same density and thickness via a massless chain that does not slip (position is given in meters and time is given in seconds). What is the ratio of the kinetic energy of the green disk to the kinetic energy of the red disk (\(KE_{\text{green}}/ KE_{\text{red}}\))? Restart.
Exercise \(\PageIndex{10}\): Two identical masses are hung over two different pulleys
Two identical black masses, \(m\), are hung via massless strings over two pulleys of identical mass \(M\) and radius \(R\), but different mass distributions as shown in the animation (position is given in centimeters and time is given in seconds). The bearings in the pulleys are frictionless, and the strings do not slip as they unwind from their pulleys. Restart.
- Which mass has the greater acceleration?
- Which pulley has the greater moment of inertia?
- Which pulley has the greater tension acting on it?
- Which pulley has the greater torque acting on it?
Answer the following in terms of a general formula for either pulley using the following variables:
\(a\) (the acceleration of the black mass), \(g,\: m,\: M,\) and \(R\).
- What is the tension in the string?
- What is the torque acting on the pulley?
- What is the moment of inertia of the pulley? Remember that we do not know the pulley's mass distribution.
Problem authored by Aaron Titus and Mario Belloni.
Exercise \(\PageIndex{11}\): A modified Atwood's machine with a real pulley
A \(1.0\text{-kg}\) cart (not shown to scale) on a low-friction track is connected to a string and a \(0.5\text{-kg}\) hanging object as shown in the animation (position is given in meters and time is given in seconds). The pulley has a uniform mass distribution in the shape of a disk and therefore affects the motion of the system. Restart.
- What is the acceleration of the system?
- What is the tension in the string? (There are two regions of the string to consider.)
- What is the mass of the pulley?
- What is the moment of inertia of the pulley?
Note that the coordinates for each object (the positive \(x\) direction) are already chosen for you.
Problem authored by Aaron Titus.
Exercise \(\PageIndex{12}\): Two masses are attached with a massless string over a pulley
Two masses, one on a table, \(M = 2.5\text{ kg}\), and one hanging, \(m = 1.0\text{ kg}\), are attached with a massless string over a pulley as shown in the animation (position is given in meters and time is given in seconds). The table is frictionless, the bearings in the pulley are frictionless, and the string does not slip on the pulley. What is the moment of inertia of the pulley? You may use either torque/force or energy methods. Restart.
Exercise \(\PageIndex{13}\): A red disk is connected by a string to a hanging mass
A \(2.5\text{-kg}\) rotating red disk is connected by a string over a pulley of mass \(m = 1\text{ kg}\) to a black hanging mass as shown in the animation (position is given in centimeters, time is given in seconds, and velocity is given in centimeters/second). The post the red disk sits on is massless and has frictionless bearings. The string is wrapped around the post and does not slip. The bearings in the pulley are frictionless and the string does not slip. What is the black block's mass? You may use either force/torque or energy methods. Restart.
Exercise \(\PageIndex{14}\): Calculate the angular momentum of several rotating objects
Each animation shows an object rotated about a fixed axis through the center (position is given in meters and time is given in seconds). Every object has the same mass, \(m = 2\text{ kg}\). Every animation has a black dot in the center indicating the origin of the coordinate system. You are to calculate the angular momentum about this point for each animation. Calculate and rank (from greatest to least) the angular momentum (about the origin) of the objects in each animation. Restart.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.
