uniform circular motion. circular motion uniform circular motion occurs when an object travels in a...
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Uniform Circular Motion
Circular MotionUniform circular motion occurs when an object travels in a circular path at a constant speed.
Uniform circular motion
Instantaneous velocity
acceleration
Q. Explain why a ball moving in a circle must be accelerating towards the centre.
A. - Magnitude of velocity is constant - Direction of velocity changes- Thus v is changing so it must be accelerating.
Centripetal force
Any acceleration must be caused by a force. In circular motion, centripetal acceleration is caused by the centripetal force (which acts towards the centre of the circle).
v
Centripetal force
Q. Explain what provides the centripetal force upon the following objects moving in circular motion:a. A planetb. An electronc. A cornering cyclistd. A banking aircrafte. ‘Wall of death’ motorcyclistf. The clothes in a spin drier
Circular Motion Calculations
Centripetal acceleration is calculated using the formula…
Thus, using F = ma
Note that using the speed formula we can say…where…
a = v2
r
v = tangential velocity at any instant (ms-1)r = radius of circle (m)a = centripetal acceleration (ms-2)
Centripetal force = mv2
r
v = 2πr T
T = 1 f
Q. What would be the effect of reducing the centripetal force for a car cornering at a fixed velocity?
E.g.1
A stone of mass 0.5kg on the end of a string 250cm long is swung in a horizontal plane at a constant speed of 10ms-1. What is the tension in the string?
A. F = mv2
r= 0.5 x 102
2.5= 20N
Vertical Circular Motion
When moving at a constant speed in a vertical circle, the centripetal acceleration and centripetal force must both be constant. A
D
C
B
mg
mg
mg
mg
T
TT
T
E.g. A bucket swinging vertically on a string:
At A:
The tension is smallest because part of the centripetal force is provided by the weight.
At C:
The tension is greatest because the tension must hold up the weight as well as supply the centripetal force.
At B and D:
The tension provides all of the centripetal force as the weight is perpendicular to the tension.
A
D
C
B
mg
mg
mg
mg
T
TT
T
At A:
mv2/r = mg + T
At C:
mv2/r = T – mg
At B and D:
mv2/r = T
Rollercoaster Physics
Q. Consider the forces acting on a rollercoaster at the top and bottom of its motion. Can you write equations describing the centripetal force similar to the last example?
B
A
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