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## Rotational Motion Exam2 and Problem Solutions

**Rotational Motion Exam2 ****and Problem Solutions**

**1.** An object in horizontal rotates on a circular road with 10m/s velocity. It does 120 revolutions in one minute.

**a)** Find frequency and period of the object.

**b)** Find the change in velocity vector when it rotates 600, 900 and 1800.

**a)** 60s.f=120 revolution

f=2 revolution/second

T=1/f=1/2s

**b) **

If object starts its motion from point A and rotates 60^{0} and comes point B;

**ΔV=V _{B}-V_{A}**

** ΔV=2V.cos120 ^{0}/2=2.10.cos60^{0}=20/2=10m/s**

If object rotates 90^{0};

If object rotates 180^{0};

**2.** A device does 1800 revolution in 6 minutes. Find angular velocity and period of this device. (π=3)

**1800.T=6.60s**

**T=360/1800=1/5s**

**ω=2π/T=2.3/1/5=30 radian/s**

**3.** Friction constant of a circular road, having radius 50m, is 0,2. Find the initial velocity of the car having 1500 kg to turn junction safely.

**Ffriction≥Fcentripetal (for safe turn)**

**k.m.g≥m.V ^{2}/r**

**k.g.r≥V ^{2}**

**100≥V ^{2}**

**10m/s≥V or**

**36km/h≥V**

**4. **A marble is thrown with velocity V from point A. If no force is exerted on surface by marble at point B, find the force exerted on point A by marble. (Assume that velocity of marble is constant.)

Since no force is exerted on point B by marble;

**mg=mV ^{2}/R**

**V ^{2}=g.R**

Force exerted by marble on point A;

**FA=G+F**

**FA=mg+mV ^{2}/R (we put V^{2}=gR into the equation)**

**FA=mg+mgR/R**

**FA=2mg**

**5.** Two objects rotate with same frequency around point O. One of the objects has mass m and other one has mass 9m. If centripetal forces exerted on objects having mass m is F1, and object having mass 9m is F2, find ratio of F1/F2.

**V _{1}=2.π.r.f**

**V _{2}=2.π.3r.f**

**V _{2}=3V_{1}**

**F _{1}/F_{2}=mV_{1}^{2}/r/9mV_{2}^{2}/3r=V_{1}^{2}/r.3r/9V_{2}^{2}**

**F _{1}/F_{2}=1/27**

Author: Mrs. Şerife (Erden) SARICA

Tags: Tangential Speed Velocity | Angular Velocity | Properties of Waves | Waves Cheatsheet | Rotational Motion Exam1 and Problem Solutions |

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