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15 Common Problems of Circular Motion

physics.fisikastudycenter.com - Learning circular motion in 15 common problems. Expressing quantities of circular motion in different units, angular speed, angular position, centripetal acceleration, centripetal force and some gears relationships will be discussed.

Problem 1
Express in radians :
a) 90o
b) 270o


Solution
360o = 2π radians

a) 90o



b) 270o


Problem 2
Express in rad/s :
a) 120 rpm
b) 60 rpm

Answer
1 rpm = 1 revolution per minute
1 revolution equals 2π radians or
1 revolution equals 360o
1 minute equals 60 sec
a) 120 rpm



b) 60 rpm



Problem 3
A particle moves at 50π rad/s of angular speed. Find the frequency of the particle motion!

Answer


Problem 4
The angular speed of a particle in circular motion is 12 rad/s. Find the speed of particle if the radius = 2 m!

Answer


Problem 5
A mass of 1 kg rotates with an angular speed of 120 rpm. If its radius is 2 meter then find the centripetal acceleration of this particle!

Answer
Data :
ω = 120 rpm = 4π rad/s
r = 2 meter
m = 1 kg
asp = ...?

asp = V2/r = ω2 r
asp = (4π)2 (2) = 32π2 m/s2

Problem 6
Find the centripetal force acting on a body of 1 kg in a circular motion with its radius of 2 m and speed of 3 m/s!

Answer
Data :
m = 1 kg
r = 2 meter
V = 3 m/s
Fsp = ....?

Fsp = m ( V2/r )
Fsp = (1)( 32/2 ) = 4,5 N

Problem 7
Given two sprockets of a bicycle as shown below!



The first sprocket radius and the second are 20 cm and 10 cm respectively and the angular speed of the first sprocket is 50 rad/s, find the second sprocket angular speed!

Answer
Data :
r1 = 20 cm
r2 = 10 cm
ω1 = 50 rad/s
ω2 = ...?

The two sprockets have the same in linear speeds if the chain does not slip or stretch so then :




Problem 8
Two rotating gears!



The speed of the first gear is 20 m/s with radius of the first and the second gears are 20 cm and 10 cm, find the second gear speed!

Answer
The two gears in the obove relationship have the same in angular velocities:



Problem 9
Three gears are configurated as below!



The radius are :
r1 = 20 cm
r2 = 10 cm
r3 = 5 cm
If the angular speed of the firs gear is 100 rad/s, find the angular speed of the third gear!

Answer

Problem 10
A particle in a circular motion has its angular speed of 4 rad/s. Determine the angular position at t = 5 sec!

Answer
Finding the angular position:
θ = ωt
θ = (4)(5) = 20 radian.

Problem 11
A particle in circular motion initially at rest. The particle angular acceleration is 2 rad/s2. Find :
a) the angular speed at t = 5 sec
b) the angular position at t = 5 sec

Answer
Data :
α = 2 rad/s2
ωo = 0
t = 5 sekon
Uniformly accelerated circular motion
a) ωt = ωo + αt
ωt = (0) + (2)(5) = 10 rad/s

b) θ = ωot + 1/2 αt2
θ = (0)(5) + 1/2 (2)(5)2

Problem 12
A car of 2000 kg of mass at 20 m/s of speed travels in circular motion with its radius of 100 m.


Find the normal force acting on the car in the peak point (the highest)!

Answer
Free body diagram of forces at the highest point :



Newton's law :



Problem 13
A particle in circular motion with its radius of 50 cm shown below.

If the mass of particle is 200 gram and the acceleration due to gravity is 10 m/s2, find the tension of the rope when it is in the highest point!

Answer

Newton's law for rotating bodies:


The free body diagram shown

So then :



Problem 14
Use the previous problem, find the tension of the rope when it is in the lowest point!

Answer:



Problem 15
Find the angular speed of the second gear!



Answer

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