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## Rotational Motion Exam1 and Problem Solutions

**Rotational Motion Exam1 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 37^{0}, find the tangential velocity of the object. (g=10m/s_{2}, cos37^{0}=0,8, sin37^{0}=0,6)

Free body diagram of system is given below;

Horizontal component of tension on the rope makes object rotate.

**T _{X}=mV^{2}/r, T_{Y}=m.g **

Radius of the motion path is;

**r=L.sin37 ^{0}=0,5.0,6=0,3m **

**tan37 ^{0}=T_{X}/T_{Y}**

**3/4=mV ^{2}/r/m.g **

**3/4=V ^{2}/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.V ^{2} **

**V=ω.r **

**EK=1/2m(ω.r) ^{2} **

**EK=mω ^{2}.r^{2}/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.ω ^{2}.r **

**80=m.4.π ^{2}.f^{2}.r**

** 80=0,5.4.3 ^{2}.f^{2}.1**

** f=2s ^{-1}**

Author: Mrs. Şerife (Erden) SARICA

Tags: Tangential Speed Velocity | Angular Velocity | Properties of Waves | Waves Cheatsheet | Rotational Motion Exam2 and Problem Solutions |

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