# 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

**ω=2.π.f=2.3.4=24radian/s**

**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**