Angular Acceleration
The translational analogue of angular acceleration.
What is linear or translational acceleration?
Moment of inertia is the rotational analogue of this quantity.
What is mass?
The formula for rotational kinetic energy.
What is 1/2(moment of inertia)(angular velocity)^2?
If an object is rotating at a constant angular velocity, what type of equilibrium is it in?
What is rotational equilibrium?
A wheel spins about a fixed axis at a constant angular speed of 5 rad/s. This is its angular acceleration.
What is zero?
The relation between angular and translational acceleration.
What is a = r(alpha)?
Formula for the moment of inertia of a point mass.
What is mr^2?
A uniform sphere of negligible mass rolls down a smooth inclined ramp. Derive the initial total energy equation for the system.
What is mgh?
A uniform 2m rod of mass 2 kg (pivoted about its left end) is held in place by a brick placed under the rod's center of mass. What is the magnitude of the brick's force?
What is 20 N?
A 2m door is pivoted about a hinge located at its left end. A force with magnitude 5 N at the right end swings it open, making the door move counterclockwise when viewed from above. What is the torque on the door?
What is 10 N-m?
A wheel rotating about a fixed axis of negligible mass starts from rest and rotates at an angular acceleration of 5 radians per second squared. In three seconds, how many radians does it rotate?
What is 22.5 radians?
Consider two identical, uniform rods. One rod is held about its center of mass and the second is held about its left end. Which has the higher moment of inertia?
What is the second rod?
A hollow, uniform sphere of radius 5 m rotates about a fixed axis. What is the rotational energy of this sphere?
What is 1/2(2/3mr^2)(5)^2 = 25/3mr^2?
If an object is in rotational equilibrium, can it still rotate? If so, what does it need to rotate with?
What is a constant angular velocity?
A uniform top with rotational inertia I and mass M spins about its center of mass. A toddler breaks it, causing the axis of rotation to shift three millimeters to the right. What is its new rotational inertia?
What is I + (M)(0.003)^2?
A wheel starts rotating with an angular velocity of 15 rad/s. It accelerates uniformly to eventually rotate 70 radians. In a 2-second timeframe, what was its final angular velocity?
What is 55 radians per second?
Two identical rods are combined (each of mass M and radius R). They are attached to each other at a 90 degree angle. What is the new total moment of inertia?
What is 2/3Mr^2?
A uniform rod of length R and mass m is pivoted about its right end and allowed to fall counterclockwise. What is the conservation of energy equation for the system?
What is mgR/2 = 1/6m R^2 w^2?
A wheel rotates with a constant angular velocity about a stationary axle of negligible mass with rotational inertia 0.5 kg m^2. Is the object in translational equilibrium, rotational equilibrium, or both?
What is translational equilibrium?
A thin uniform wheel rotates about a fixed axis of negligible mass. The wheel has a radius of 4 meters, a mass of 4 kilograms, and a net counterclockwise torque of 8 N-s acting on it. What is its angular acceleration? What is its angular acceleration after an outside force of 6.7N acts on the edge of the wheel against the counterclockwise torque?
What is 0.125 rad/s/s and -0.29 rad/s/s?
An object moves with an angular jerk represented by the function 2t^3 (after starting from rest). Find the object's angular acceleration at 4 seconds.
What is 128 radians per second squared?
A solid, uniform hoop of mass M and radius r has a rotational inertia about its center. If this moment of inertia is shifted 5 meters from its original location what is its new moment of inertia?
What is I = Io + Md^2 = Mr^2 + 25M = M(r^2+25)?
Two identical, solid hoops rotate with the same angular velocity. One rotates about its center and the second rotates about a point located 0.5 meters from its center. Each hoop is of rotational inertia I, mass M, and radius R. Which one has more rotational kinetic energy?
What is the second disk?
What is 262.2 Newtons?
Mr. Holloway is building a massive bridge using a nonuniform rod of length L, with a linear density given by the equation λ(x)=λ(1+Lx). Using this equation, find the total mass of the rod.
What is mass = λ(L + L^3/2)?