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How do you calculate net torque?
Add up all the individual torques acting on the object as vectors. $\sum \tau = \tau_1 + \tau_2 + ...$
How do you calculate rotational inertia for a system of point masses?
Use the formula: $I = \sum mr^2$, where m is the mass of each point and r is its distance from the axis of rotation.
How do you relate linear and angular speed for rolling without slipping?
The linear speed of the center of mass is related to the angular speed by $v_{cm} = R\omega$, where R is the radius of the object.
How do you determine the direction of angular acceleration?
The direction of the angular acceleration is the same as the direction of the net torque vector. Clockwise torque results in clockwise angular acceleration, and counterclockwise torque results in counterclockwise angular acceleration.
What is the first step in solving rotational dynamics problems?
Draw a free body diagram showing all forces acting on the object and their points of application.
Label the forces acting on the block in the diagram.
1: Tension (T) upwards, 2: Weight (mg) downwards
Label the forces acting on the disk in the diagram.
1: Tension (T) tangential, 2: Weight (Mg) downwards, 3: Normal force (N) upwards
In the diagram of a hollow vs. solid cylinder rolling down an incline, which has greater rotational inertia?
The hollow cylinder has a greater rotational inertia.
Define torque.
The rotational equivalent of force; what causes an object to start rotating or change its rotation.
Define rotational inertia.
A measure of how much an object resists changes in its rotational motion.
What is angular acceleration?
The rate of change of angular velocity.
Define Newton's Second Law for Rotation.
The net torque on an object is equal to the product of its rotational inertia and angular acceleration: $\sum \tau = I \alpha$.
What is tangential speed?
The linear speed of a point on a rotating object, related to angular speed by $v = r\omega$.
What is tangential acceleration?
The linear acceleration of a point on a rotating object, related to angular acceleration by $a = r\alpha$.