Rotational Kinematics
This is the rotational version of linear displacement, typically measured in radians.
What is angular displacement?
This is the standard SI unit used to measure torque
What is the Newton-meter
A measure of an object's resistance to changes in its rotational motion, analogous to mass in linear motion
What is rotational inertia (or moment of inertia)?
For an object to be in rotational equilibrium, the sum of all external torques acting on it must equal this value.
What is zero?
What are the rotational counterparts to force, mass, and linear acceleration in Newton’s Second Law?
Torque (τ), Moment of Inertia (I), and Angular Acceleration (α).
An object's angular velocity changes from 10 rad/s to 20 rad/s in 5 seconds. This is its average angular acceleration in rad/s
2 rad/s^2
To maximize the torque applied to a bolt using a wrench, you should apply the force at this angle relative to the wrench handle
What is 90 degrees (or perpendicular)
Daily Double
The mathematical expression for the rotational inertia of a single point mass m rotating at a radius r from the axis of rotation.
What is I=mr^2
The name for the rotational equivalent of linear force.
What is torque?
If the net torque applied to a rigid body is tripled while its moment of inertia remains constant, what happens to its angular acceleration?
The angular acceleration will also triple, as α is directly proportional to the net torque.
This is the equation that relates tangential velocity to angular velocity and the radius for an object undergoing rotational motion.
For a rigid body to be in static equilibrium, both the net force acting on it and this value must be equal to zero.
What is the net torque
Between a solid sphere and a hollow sphere of the same mass and radius, this object has a larger rotational inertia when rotating about an axis through its center.
What is the hollow sphere?
Newton's First Law for rotation states that a spinning object will continue spinning at a constant angular velocity unless acted upon by a non-zero this.
What is net external torque?
A uniform disk with a moment of inertia of 4 kg⋅m^2 is acted upon by a constant net torque of 8 N⋅m. What is the resulting angular acceleration?
2 rad/s^2
A turntable initially at rest is set in motion with a constant angular acceleration a. After it makes one complete revolution, its angular velocity is given by this expression in terms of a
A 50 N force is applied to a 2-meter long rod at an angle of 30 degrees to the rod’s surface. This is the magnitude of the torque produced about the pivot at the end of the rod.
What is 50 N·m
A disk and a hoop, both with identical mass and radius, are released from rest at the top of an incline and roll down without slipping. Which one reaches the bottom of the incline first?
The disk [because it has a smaller rotational inertia compared to the hoop and thus converts more potential energy into translational kinetic energy]
The perpendicular distance from the axis of rotation to the point where a force is applied is known by this two-word term.
What is the lever arm (or moment arm)?
A 20 kg door, 1.0 m wide, is hinged at one end (I=1/3ML^2). If a 15 N force is applied perpendicular to the door at its outer edge, what is the angular acceleration?
2.25 rad/s^2
A wheel with radius 0.5 m is accelerated uniformly from rest to an angular velocity of 4.0 rad/s in 2.0 s. This is the tangential acceleration of a point on the outer edge of the wheel.
1.0 m/s^2
This is the rotational equivalent of Newton’s Second Law (F=ma), relating net torque to rotational inertia and angular acceleration
What is ∑τ=Iα?
According to the parallel axis theorem, if Icm is the moment of inertia about the center of mass, M is the total mass, and d is the perpendicular distance to a new parallel axis, what is the formula for the new moment of inertia (I)?
An object is in static equilibrium when it satisfies these two conditions: net force is zero and net torque is zero.
What are translational and rotational equilibrium?
Daily Double
A block of mass m is hanging from a string wound around a pulley of mass M and radius R (I=1/2MR^2). If the block is released from rest, what is the expression for the angular acceleration of the pulley?
α=mg/R(m+1/2M)