Now that we've learned about torque, let's learn how it causes rotational motion (or no motion).

First, we need to find the net torque that is acting on an object. This just means adding up the individual torques from the individual forces acting on the object. We usually consider counterclockwise torques to be positive and clockwise torques to be negative.

Then we need to know the object's rotational inertia, sometimes called its moment of inertia. Just like every object with mass has inertia (resistance to linear acceleration), every object also has rotational inertia (resistance to rotational acceleration). The rotational inertia depends on how far the object's mass is distributed from the axis of rotation. If you've ever noticed that you automatically stick your arms out to balance yourself, this is your body trying to increase your own rotational inertia.

Finally, we can apply Newton's 1st and 2nd laws of motion to rotational motion. Just like how a net linear force causes a mass to have a linear acceleration, a net torque causes a mass to have an angular (rotational) acceleration.

Even if an object has several torques acting on it, the object might not rotate. From Newton's 1st law of motion, we learned that if the forces are balanced and the total net force on an object is zero, there is no acceleration. Likewise, if the torques applied to an object are balanced and the total net torque is zero, there is no rotational acceleration. We call that rotational equilibrium.

Multiple-Choice Questions

Answers

- Net Torque

• Michel van Biezen - How to Calculate the Net Torque Ex 1
• Michel van Biezen - How to Calculate the Net Torque Ex 2

- Equilibrium and Angular Acceleration

• Michel van Biezen - Torque and Angular Acceleration
• Flipping Physics - Introductory Rotational Form of Newton's Second Law

- Rotational Inertia (Moment of Inertia)

• Khan Academy - Moment of inertia
• Flipping Physics - Demonstrating Rotational Inertia (Moment of Inertia)
• Flipping Physics - Moments of Inertia of Rigid Objects with Shape
• Matt Anderson - Moment of Inertia

• Michel van Biezen - The Diving Board
• Michel van Biezen - Mass on Rod and Cable
• Organic Chemistry Tutor - Static Equilibrium

• Veritasium - The Bizarre Behavior of Rotating Bodies
• Optimizing Moment of Inertia for Spinnable Objects

• Moment of Inertia On Incline
• Moment of Inertia and Torque
• Equilibrium, Bar and Cable
• Static Equilibrium

Other Resources

Now that we've learned about torque, let's learn how it causes rotational motion (or no motion).

First, we need to find the net torque that is acting on an object. This just means adding up the individual torques from the individual forces acting on the object. We usually consider counterclockwise torques to be positive and clockwise torques to be negative.

Then we need to know the object's rotational inertia, sometimes called its moment of inertia. Just like every object with mass has inertia (resistance to linear acceleration), every object also has rotational inertia (resistance to rotational acceleration). The rotational inertia depends on how far the object's mass is distributed from the axis of rotation. If you've ever noticed that you automatically stick your arms out to balance yourself, this is your body trying to increase your own rotational inertia.

Finally, we can apply Newton's 1st and 2nd laws of motion to rotational motion. Just like how a net linear force causes a mass to have a linear acceleration, a net torque causes a mass to have an angular (rotational) acceleration.

Even if an object has several torques acting on it, the object might not rotate. From Newton's 1st law of motion, we learned that if the forces are balanced and the total net force on an object is zero, there is no acceleration. Likewise, if the torques applied to an object are balanced and the total net torque is zero, there is no rotational acceleration. We call that rotational equilibrium.