Physics

Rotational Energy & Static Equilibrium

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A Summary So Far

Kinematics:

Dynamics:

Energy:

Momentum:

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Constant Acceleration

Rotational Kinetic Energy

Consider our old pal the uneven dumbbell…

What kinetic energy does the system have?

So, rotational kinetic energy must then be:

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Energy of a Rigid Body

The energy for a cluster of masses can be generalized to a continuous object:

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Axis of Rotation

Whiteboard Problem 12-12

A 300g ball and a 600g ball are connected by a 40cm long massless, rigid rod to form a dumbbell. The dumbbell rotates around its center of mass at 100rpm.

What is the rotational kinetic energy of the dumbbell? (LC)

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Static Equilibrium

For objects that aren’t points, equilibrium is a bit different.

This is a future you problem.

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FBD:

x

y

Previously in PHY191…

6_2, slide 15

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Static Equilibrium

A body is in static equilibrium if:

Torque about any point must be zero.

Side note: forces acting at a pivot point produce 0 torque.

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A note on Gravity

Gravity can exert a force, but what about a torque?

Gravity acts over the entire body.

Whenever you’re solving a problem, know that gravity will effectively act at the center of gravity of an object.

This is the same location as the center of mass for all of the objects we will consider in this class.

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Solving Static Equilibrium Problems

Picture

Reference Frame

Including rotation direction (CCW +)

Draw a FBD

Sum the forces in all directions

They sum to zero

Sum the torques about a point (usually a pivot)

They sum to zero

Solve

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A beam of mass M and length L is resting on a pivot as shown below:

What must the force F be in order to keep the beam still?

Example

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Whiteboard Problem 12-10

The two blocks of citrine shown below have uniform density and are balanced on the pivot.

Draw Free Body Diagrams for both blocks. What is the force of the upper block on the lower block?

Use the FBD of the lower block to find the distance d. (LC)

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That’s about 15,000$ of citrine.

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Whiteboard Problem 12-11

In the figure below, an 80kg construction worker sits down 2.0m from the end of a 1450kg steel beam to eat his lunch. The cable supporting the beam can withstand a maximum tension of 15,000N.

Draw a FBD of the beam.

Determine the tension in the cable (LC) – does the cable break?

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Live Action Science

What is the mass of a meter stick?

On Canvas, find the assignment labeled Meter stick mass, make a copy of the google document and share it with your group.

Using the materials on the wire rack on the East side of the room, determine a method using what we’ve learned so far this week to determine the mass of a meter stick. Record your process on the google doc.

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