circular motion. period and frequency a cd rotates in a player at a constant speed of 240 rpm....
TRANSCRIPT
Circular Motion
Period and Frequency
• A CD rotates in a player at a constant speed of 240 rpm.– How frequently does it complete a revolution:
• In minutes?
• In seconds?
– How long does it take to complete one revolution?
Period and Frequency
• Period (T): The time it takes for an object in circular motion to make one complete revolution (or cycle)– Unit: s/rev– s/cycle– seconds
• Frequency (f): The number of revolutions, or cycles, in a given period of time– Equation:– Unit: 1/s – s-1
– Hertz (Hz)
Speed of an Object traveling in a Circle
• A car traveling in a circle with a radius of 40 m. – How far does it travel per cycle?
•
• The car completes 5 revolutions per minute.– What is its period? (How long does it take to complete a rev?)
•
• What is the car’s speed?
–
5 m
10 m
Each Revolution takes 2 seconds
What was the distance traveled by box 1? 2
1
What was the distance traveled by box 2?
What was the speed of box 1?
What was the speed of box 2?
Centripetal Acceleration
• Velocity is a Vector– Magnitude (i.e. size)– Direction
– Speed is constant, direction changing with time Velocity is changing with time, thus accelerating
v
vAfter 2 Secv
After 3 Sec
vAfter 6 Sec
After 5 Secv
After 4 Sec v
After 7 Sec
v
• Centripetal Acceleration: The acceleration of an object traveling in a circle at a constant speed– Speed is constant– Direction is changing– Acceleration vector points inward (center
seeking)
Centripetal Acceleration
v
ac
vf-vi
Centripetal Acceleration
• Why does the acceleration vector point inward?
vi
vf
vi-vi
vf
-vi
Centripetal Force
• ac, centripetal acceleration (m/s2)– “Center seeking”– Necessary to keep the object traveling in a circle
• Fc, centripetal force (N)
– Newton’s 2nd Law
• Newton’s 2nd Law for Circles
• NOTE: CENTRIFUGAL FORCE IS AN IMAGINARY FORCE TO EXPLAIN INERTIA! DOES NOT EXIST!
Centripetal Force
• The centripetal acceleration is caused by another force such as:– Friction– Tension– Normal Force– Gravity
Centripetal Force
• Steps to solve centripetal force problems:– Draw a free body diagram – Identify the force causing the centripetal force
• The force that is keeping the object going in a circle
– Set the causal force = centripetal force eq.– Solve for unknown
A 0.50 kg box is attached to string on a frictionless horizontal table. The box revolves in a circle of radius 2.8 m. If the box completes 1 revolution every 2.0 seconds, what is the tension in the string?
r
The centripetal force is caused by… the tension in the string
FN
Fg
FT
We know m & r, but need v
A 1200 kg car approaches a circular curve with a radius of 45.0 m. If the coefficient of friction between the tires and road is 1.20, what is the maximum speed at which the car can negotiate the curve?
r
FN
Fg
Ff
(Car is going into the page and turning right)
The centripetal force is caused by… friction