If a body moves in a circle there must be a resultant force acting towards the centre. This is because the change in direction implies that the body is accelerating.
Deriving the equation is not so simple though...
Key Concepts
When deriving the equation for centripetal acceleration we start by considering a small part of the motion we can deduce that
\(a = {mv^2\over r}\)
This is the acceleration.
Use quizzes to practise application of theory.
START QUIZ!
Fill in the blanks of this justification that the force causing a body to move around a circle at constant speed must be towards the centre.
Word list: 1st, 2nd 3rd, direction , perpendicular, parallel, force, tangential, radial, kinetic, potential, work, acceleration
When a body travels in a circle its is always changing so it must have . According to Newtons law there must be an unbalanced force acting on it.
If the speed is constant then the energy must be constant which means no is being done on the body.
done = x distance moved in direction of so if no work is done the must be to the direction of motion, i.e. .
A mass on a string completes 3 revolutions in 2 seconds.
The angular velocity in radians s-1 is:
3 revs is 6π rads so ω = 6π/2
A mass travels in a circle on the end of a spring at constant speed
Which of the following statements is true
centripetal force is the name given to the force that acts towards the centre so doesn't pull the spring out, however the spring pulls the ball in so according to newt 3 the ball must pull the spring out.
A ball moves in a circle of radius 2 m with constant speed 2 ms-1.
The time to complete 1 revolution is:
distance travelled in 1 revolution = 2πr
t = d/v = 2π x 2/2
10° in radians is about
10/360 x 2π approx 6/36 = 1/6
process of elimination, all the others are way too big
A ball on a string moves in a circle as shown
The magnitude of change in velocity is:
Must calculate change vectorially so use Pythagoras.
A mass travels in a circle of radius 2 m with constant speed 3 ms-1.
The acceleration of the mass is:
a = v2/r
If a = v2/r and v = ωr then:
a = ω2r2/r =ω2r
A 2 kg mass travels in a circle of radius 5m with time period π s.
Angular velocity = rads-1
Centripetal acceleration = rads-2
Centripetal force = N
ω = 2π/T
a = ω2r
F = ma
How much of Centripetal force have you understood?
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