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Rotational dynamics

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Rotational dynamics

Chapter 8

- Up ‘til now, we have assumed that all masses are essentially points in space.
- From this point onwards, we will treat all objects as extended.

- We established earlier that centripetal force causes circular motion.
- What causes the centripetal force in the first place?

- Remember, for all objects, we are assuming that the object rotates around a fixed axis.
- Objects rotating around this axis feel the centripetal force.

- The ability of a force to rotate an object around that axis is measured by a quantity known as torque.
- Torque is dependent on three things
- Force
- Lever arm
- The angle between the two

- Depending on where the force is applied, torque will increase or decrease.
- Torque is a vector

- A mechanic applies a force of 400 N at an angle of 20 degrees on this wrench. The wrench is 0.3 meters long. What is the torque?

- Like force, there can be multiple torques on an object.
- You can add those all up to find the net, or total, torque.
- ∑τ=τ1+τ2+τ3+…
- Keep in mind each torque can be positive or negative, so the net torque will be + or –.

Find the net torque of all the forces on the triangle around the fixed point. (ignore the d’s and f’s in the diagram).

- The axis of rotation is easy to find for some objects. Doors, the windows in the back, all have hinges.
- What if something is flying through the air?

- If gravity is the only force acting on something, that object will rotate about its center of mass.
- This in turn means that airborne objects undergo both linear and rotational motion

- Depending on if the object is symmetrical or not, the center of mass is either easy or hard to find.

- It’s easier to rotate some objects around a certain axis than others.
- What’s the best way to swing a bat?

- An object’s ability to resist rotational motion is measured by its moment of inertia.
- Mass and moment of inertia both resist motion
- Mass resists linear
- M.o.I resists rotational

- How an object is shaped determines its moment of inertia.
- The further the mass is from the axis, the greater the m.o.i.