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Two ways to compute torque: 1. Put r and F vectors tail-to-tail and compute t = rFsinq. 2. Decompose F into components parallel and perpendicular to r, and take: t = rF ┴ If rotation is clockwise, torque is negative, and if rotation is counterclockwisetorque is positive. Note: If F and r are parallel or antiparallel, the torque is 0.
1 Torque In this chapter we will investigate how the combination of force (F) and the moment arm (‘) e ect a change in rotational motion (i.e., rotational angular acceleration, ). ˝ = force moment arm (de nition of torque) where the moment arm is the distance of closest approach to the line of action of the force.
The vector product is a type of “multiplication” law that turns our vector space (law for addition of vectors) into a vector algebra (a vector algebra is a vector space with an additional rule for multiplication of vectors).
Step 1 – Mark a few points on a rotating disk and look at their instantaneous velocities as the disk rotates. Let’s assume the disk rotates counterclockwise at a constant rate. Even though the rotation rate is constant, we observe that each point on the disk has a different velocity.
Or every time we move our bodies from a standing position, we apply a torque to our limbs. In this section, we define torque and make an argument for the equation for calculating torque for a rigid body with fixed-axis rotation.
Method 1: If you're given r and θ, use formula for torque (magnitude) τ = r F sinθ (Note: sinθ = sinφ, ∴ it doesn’t matter which angle you use) Calculating torque (2) Method 2: If you're given d. the “perpendicular distance” from axis to the “line of action”, then use formula τ = d F.
In the most general form, torque ( r ) is expressed as the cross product of the moment arm and the applied force. r r r. = r F . where r. is the moment arm, measured from the rotation axis to the point where the force, . , is applied (See Figure 1). The units of torque are Newton-meters (N-m). The magnitude of the torque is expressed as.
