NumericalChapter No.5

Circular MotionF.Sc 1st part

P.No.5.1:- A tiny laser beam is directed from the Earth to the Moon. If the beam is to have a diameter of 2.50m at the moon, how small must divergence angle be for the beam? The distance of Moon from the Earth is . Solution:- Given Data:- Length of arc = S = 2.50m (Diameter of beam) Radius of circular arc = r = (The distance of Moon from the Earth)To Determine:- Angle = = ?Calculation:- Using the relation.

P.No5.2:- A gramophone record turntable from rest to an angular velocity of 45.0 in 1.60s. What is its average angular velocity?

Solution:-Given Data:- Initial angular velocity =

Final angular velocity =

Time = t = 1.60sTo Determine:- Average angular acceleration = = ?Calculation:- Using the relation

P.No.5.3:- A body of moment of inertia about a fixed axis, rotates with

a constant angular velocity of . Calculate the angular momentum “L” and the torque to sustain this motion.Solution:- Given Data:- Moment of inertia =

Angular Velocity = To determine:- Angular momentum = L = ? Torque = = ?Calculation:- Using the relation

Now for calculating the torque we use Here angular acceleration is zero only because the body is moving with constant angular velocity and we know from the theory that angular acceleration is the rate of change of angular velocity so acceleration is zero and torque is also zero because torque is the product of moment of inertia and angular acceleration.

So, Problem No.5.4:- Consider the rotating cylinder shown in fig. Suppose that M=5.0kg, F=0.60N and r=0.20m. Calculate (a) Torque acting on the cylinder (b) The angular acceleration of the cylinder. (Moment of inertia of cylinder

)

Solution:-Given Data:- Mass of Cylinder = M = 5.0kg

Force acting on cylinder = F = 0.60N Radius of cylinder or the distance from the point of application of force to the axis Of rotation = r = 0.20mTo Determine:-

P.No.5.5:- Calculate the angular momentum of a star of mass and

radius . If it makes one complete rotation about its axis once in 20 days, what is its kinetic energy?Solution:-Given Data:-Mass of star = M =

Radius of star = Time period of star = T = 20days To Determine:- Angular momentum of star = L = ? Kinetic energy = K.E = ?Calculation:- For part (a) Using the relation for angular momentum

For part (b) using the relation of kinetic energy

P.No.5.6:- A 1000kg car traveling with a speed of 144 rounds a curve of radius 100m. Find the necessary centripetal force.Solution:-Given Data:- Mass of the car = M = 1000kg

Speed of car = v =

Radius of the curve = r = 100mTo Determine:- Centripetal force = Fc = ?Calculation:- Using the relation.

P.No.5.7:- What is the least speed at which an airplane can execute a vertical loop of 1.0km radius so that there will be no tendency for the pilot to fall down at the highest point?

Solution:-Given Data:- Radius of loop = R = 1.0km = 1000m Acceleration due to gravity = g = To Determine:- Speed of airplane = v = ?Calculation:- Using the relation

P.No.5.8:- The Moon orbits the Earth so that the same side always faces the Earth. Determine the ratio of its spin angular momentum (about its own axis) and its orbital angular momentum. (In this case, treat the moon as a particle orbiting the Earth). Distance between the Earth and the Moon is . Radius of the Moon is .Solution:-Given Data:- Distance between Earth and Moon = r =

Radius of the moon = To Determine:-

Ratio of spin and orbital angular momentum = = ?

Calculation:- Using the relation

P.No.5.9:- The Earth rotates on its axis once a day. Suppose, by some process the Earth contracts so that the radius is only half as large as at present, how fast will it be rotating them?

(Moment of inertia of sphere )

Solution:-Given Data:- Time period = 24 hr

Moment of inertia =

Radius of earth = (Given)

To Determine:- How fast will the Earth be rotating = ?Calculation:- Using the relation.

P.No.5.10:- What should be the orbiting speed to launch a satellite in a circular orbit 900km above the surface of the Earth? (Take the mass of Earth as and its radius as 6400km )Solution:-Given Data:- Mass of Earth = M =

Radius of Earth = R = 6400km =

Height of circular orbit = h = 900km = To Determine:- Orbital Speed = v = ?Calculation:- Using the relation.

By Muzammal Safdar

Prepared By Muzammal SafdarVisit http://www.fscphysicsofpk.blogspot.com/ for online accessContact muzammalsafdar@gmail.com/