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Home , Centripetal force

2/20/15

Announcements

• Today: Torque, Angular • Torque is the rotational analog of . • Wednesday: • Depends on: • Reading: Chapter 10, focus on figs. 10.3, – Magnitude of Force 10.17, & 10.31 – Direction of force • Reminder: Midterm #1 is on Friday! – Lever arm – Topics list is posted on class website – Bring pencil, eraser, calculator, and scantron 882- • torque = lever arm x force E • Units of N!m

Examples of Lever Arm Example: Pedaling a Bicycle

• Lever arm is amount of perpendicular distance to where the force acts.

Revisiting Newton’s Laws Example: See-Saw Balancing

1: Need a linear force to change an object’s 4 m ? m linear " Need a torque to change an object’s rotational motion • Equilibrium: – Linear: ΣF = 0 – Rotational: Στ = 0 2: Translational ~ force, and ~ 1/ " ~ torque, and ~ 1/rotational

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Ranking Announcements

• Which meter • Today: Finish up stick requires • Friday: Midterm #1! the most • No reading! torque to hold up the weight?

Center of Mass Example

• Average position of all the mass in an • Three trucks are parked on a slope. Which object is called the center of mass (CM) of truck(s) tip over? object. • Average position of the weight distribution is called the center of gravity (CG). • When gravity is constant (usually the case), these two locations are the same.

Angular Momentum Conservation of

• Recall: Linear momentum = mass x If no external net torque acts on a rotating system, then the angular momentum of that system remains constant. • Angular momentum = rotational inertia x rotational velocity L = I ω • Need an to change linear momentum " need a torque to change angular momentum!

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Examples Angular Momentum

• Conservation of angular momentum plays • Special case: for an object that is small a big role in astronomy, because it relates relative to its axis of rotation ( in its tangential (or orbital speed) to , bug on a turntable) radius (or orbital distance). Angular momentum L = mvr • Formation of stars, planetary systems, and galaxies • Moon’s orbit around the Earth Units: kg m2 /s

Example: Merry-go-round Centripetal Force

• What is the angular momentum of our 75 • Centripetal means “towards the center.” kg person going 3 m/s on the merry-go- round with radius of 2 m? Whenever an object moves along a circular path, there must be a force on that object in the direction of the center of the circle.

• In such a case, the force is said to be centripetal

Centripetal Force Example: The spin cycle! • Any force directed toward a fixed center is called a centripetal force. – Centripetal means “center-seeking” or “toward the center.”

F = mv2/r

r = radius of circle v = tangential velocity

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Example (by XKCD)

You are riding at the very edge of a merry- go-round with a radius of 2 m. Your friend runs alongside, pushing the merry-go-round so that it’s tangential speed is 3 m/s. a. What force is keeping you from off? b. If you have a mass of 75 kg, what is the strength of that force?

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