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# Introduction to torque

An introduction to torque, a force that causes rotation. Understand how torque is calculated as the product of force and distance, and how it differs from work. Learn about the direction of torque and its units. Get a grasp on the concept of net torque and its role in rotational motion. Created by Sal Khan.

## Want to join the conversation?

• How is torque different than Work... isnt Work formula ForceXDistance?

Can you give an example besides Sal's? • Okay, so here I am going to assume you have a decent amount of knowledge about dimensions. Now, your confusion lies in the thinking the because both Work and Torque have the same Physical Quantities(Force and distance) being multiplied together, they must be the same. Even though both Work and Torque have the same dimensional formula ([M][L]^2[T]^2) they are not the same. Why? Because to find out Work, you multiply the Force by the Distance through which it has accelerated, and that too, using the DOT PRODUCT method, Whereas while calculating Torque, you CROSS PRODUCT the force that you apply and it's distance from the 'pivot'. I really tried mt best to explain this without a diagram. Whether you understand what I just said explained depends on how much you know about vectors and dimensions. Good Luck :-)
• Let's say there is a stationary ruler floating in space and I apply a force to one end of it. Wouldn't it both rotate around its center of mass AND move slightly in the direction of my force? Does the movement in the direction of my force simply lessen while rotation increases, as I move farther away from the center of mass? •  Yes, it will have both rotational and translational motion.
Yes, as you move away from the center of mass, more energy will be put into rotation versus translation so the ruler will spin more and the COM will be displaced less.
Good question!
• What exactly is torque? I know it's Force x Distance, but what does one mean when it is said "an object has torque"? From what I've found so far, the definition is pretty vague. • The others are right: torque is just another form of force. For example, Sal emphasizes that when the net torque on an object is 0, the rate of rotation remains constant. Compare this to when we said "when the net force on an object is 0, the rate of change of displacement (i.e. velocity) remains constant".

As you see, torque is the force, rotation is circular displacement, and rate of rotation is the speed of spinning.
• At school, I have learnt that the equation is "Torque=Fd sin(theta)". Can I please ask when I am supposed to include angle? • In high schools the formula is usally shown as "torque=force*distance" because we assume that there is a right angle between the force and the lever arm. The other formula is more general, and takes into account when the angle theta is not 90 degrees (sin90=1). Hope that helps.
• how do you calculate the force if it is not perpendicular to the turning point? i.e instead of coming in at 90 degrees its 70 degrees • I came to this video when I was reading about gears. I mathematically understand that gears can be used to control speed and torque. But won't application of more torque just mean more acceleration and hence more speed? It just doesn't make intuitive sense. • I am having trouble determining if the torque of the plank is counterclockwise or clockwise. like how do we determine its lever arm and its direction • It depends on the direction of the force and the side of the pivot point or center of mass that the net force is acting upon in relationship to the viewer's eyes. If, to you the *net*force is down or closer to you on the left or up or away from you on the right of the pivot point or center of mass then the object will turn counter-clockwise. Otherwise the object will turn clockwise.
• Whats the diff b/w center of mass and center of gravity? • This is pretty self-explanatory and in case of a uniform gravitational field, they are the same, anyways. However, while the center of mass of a single rigid body is fixed in relation to the body, the center of gravity depends on the gravitational field, the body is in. If the field is not uniform, gravity will 'pull on' some parts of the body more, than it does on others...  