Angular Acceleration, Rotational Inertia, and Torque

Front

What are the rotational equivalents of distance, velocity, and acceleration?

Back

θ (angle), ω (angular velocity), α (angular acceleration)

Front

Which solid ball reaches the bottom of an incline first: a ball of radius R and mass M or a ball of radius 2R and mass 8M?

Back

The small sphere (radius R) arrives first.

Front

How can you achieve maximum torque?

Back

By using a longer lever arm and applying more force perpendicularly.

Front

If two wheels are fixed to each other and four forces are exerted tangentially, what direction will they rotate if the net torque is clockwise?

Back

The wheels will rotate clockwise.

Front

What is the magnitude of the net torque if two wheels are fixed to each other and four forces are exerted tangentially?

Back

4FR (where F is the force and R is the radius).

Front

Define angular acceleration.

Back

Angular acceleration (α) is the rate of change of angular velocity over time.

Front

What is rotational inertia?

Back

Rotational inertia (I) is the resistance of an object to changes in its rotational motion, depending on the mass distribution relative to the axis of rotation.

Front

What is torque?

Back

Torque (τ) is a measure of the rotational force applied to an object, calculated as τ = r × F, where r is the lever arm and F is the force.

Front

How does the radius of an object affect its rotational inertia?

Back

The larger the radius, the greater the rotational inertia, as mass is distributed further from the axis of rotation.

Front

What is the relationship between torque and angular acceleration?

Back

Torque is directly proportional to angular acceleration, expressed as τ = Iα, where I is the rotational inertia.