# Rotational Motion Exam 1 and Problem Solutions

1. An object, attached to a 0,5m string, does 4 rotation in one second. Find

a) Period

b) Tangential velocity

c) Angular velocity of the object.

a) If the object does 4 rotation in one second, its frequency becomes; f=4s⁻¹

T=1/f=1/4s

b) Tangential velocity of the object;

V=2.π.f.r

V=2.3.4.0,5

V=12m/s

c) Angular velocity of the object

2. Find the relation between tangential and angular velocities of points X, Y and Z. X and Y rotate together, so if X does one rotation then Y also does one rotation. On the contrary, if Y does one revolution, Z does two revolutions. Angular velocities of the X, Y and Z are;

ωX=ωY=ωZ/2

3. An object hanged on a rope L=0,5m, does rotational motion. If the angle between rope and vertical is 37⁰, find the tangential velocity of the object. (g=10m/s², cos37⁰=0,8, sin37⁰=0,6) Free body diagram of system is given below; Horizontal component of tension on the rope makes object rotate.

Tx=mV²/r, Ty=m.g

Radius of the motion path is;

r=L.sin37⁰=0,5.0,6=0,3m

tan37⁰=Tx/Ty

3/4=mV²/r/m.g

3/4=V²/g.r

V=3/2m/s

4. An object having mass m does rotational motion. Its angular velocity is ω and radius of motion path is r. Find kinetic energy of the object in terms of r, ω, and m.

EK=1/2m.V²

V=ω.r

EK=1/2m(ω.r)²

EK=mω².r²/2

5. Stone having mass 0,5kg rotates in horizontal. It is hanged on 1m rope. If the tension on the rope is 80 N, find the frequency of the motion.

Fnet=80N=m.ω².r

80=m.4.π².f².r

80=0,5.4.3².f².1

f=2s⁻¹