# UCM 5

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Published on March 7, 2008

Author: zglazenburg

Source: slideshare.net

UNIFORM CIRCULAR MOTION

What is UCM?

UCM is the motion of an object along a circular path at a constant speed.

UCM is the motion of an object along a circular path at a constant speed.

So What Causes an Object to move in UCM?

Centripetal force Causes an object to stay in UCM. Centripetal force is any force or sum of forces which keeps an object in UCM.

Centripetal force is any force or sum of forces which keeps an object in UCM.

REMEMBER! Centripetal acceleration and Centripetal force are directed to the center. Velocity is directed tangentially to the curvature of motion.

Centripetal acceleration and Centripetal force are directed to the center.

Velocity is directed tangentially to the curvature of motion.

EXAMPLES OF UCM

Car turning a corner

Woman on a rotor

Ball Spinning On String

Satellite in UCM

Steps for solving UCM problems

Problem If Captain Crunch is flying his 60,500kg plane in a circle whose radius is 50km, Once every 30 minutes, what is the size of its centripetal force?

If Captain Crunch is flying his 60,500kg plane in a circle whose radius is 50km, Once every 30 minutes, what is the size of its centripetal force?

Free body diagram

Step 1 Write out formulas. Fc=MAc Ac=(v^2)/r V=[2(pi)r]/T

Write out formulas.

Fc=MAc

Ac=(v^2)/r

V=[2(pi)r]/T

Step 2 Write knowns M=60,500kg r=50km=50000m t=30min=1800sec Fc=?

Write knowns

M=60,500kg

r=50km=50000m

t=30min=1800sec

Fc=?

Step 3 Put knowns into formula V=[2(pi)50,000m]/1800sec V=174.5m/s Ac=[v^2]/r=[(174.5m/s)^2]/50000m Ac=.609m/s^2 Fc=mAc Fc=60,500kg*.609m/s^2 Fc=36845N

Put knowns into formula

V=[2(pi)50,000m]/1800sec

V=174.5m/s

Ac=[v^2]/r=[(174.5m/s)^2]/50000m

Ac=.609m/s^2

Fc=mAc

Fc=60,500kg*.609m/s^2

Fc=36845N

Very Important! Centripetal force = mass x centripetal acceleration Centripetal force is directed towards the center

Centripetal force = mass x centripetal acceleration

Centripetal force is directed towards the center

Don’t Forget! Centripetal acceleration is directed towards the center Velocity is tangential to the path of motion

Centripetal acceleration is directed towards the center

Velocity is tangential to the path of motion

Finally Make sure you draw free body diagrams! They are VERY IMPORTANT!!

Make sure you draw free body diagrams!

They are VERY IMPORTANT!!

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