Mechanics | Relativity Answers

A bacteria of mass 2 × 10−24 kg is rotated in a centrifuge at an angular speed of 4p × 103 rad s−1.
It is situated at a distance of 5 cm from the axis of rotation. Calculate the effective value of g
relative to the rotating frame of reference and the net centrifugal force on the bacteria.

A wheel of mass of 30 kg and radius 1.5 m is rotating with an angular velocity of 280 rpm.
Calculate the work that must be done to bring the wheel to rest in 15 seconds. What is the
required average power?

Suppose you are designing a cart for carrying goods downhill. To maximize the cart speed,
should you design the wheels so that their moments of inertia about their rotation axes are large
or small, or it does not matter? Explain assuming that the mechanical energy is conserved.

Express the rotational kinetic energy of the earth in terms of its period of rotation. The moment
of inertia of the earth about its spin axis is 8.04 × 1037 kg m2. Calculate its rotational kinetic
energy.

When is the earth’s orbital motion around the sun fastest and when is it slowest? In which month
of the year is the earth closest to the sun? Explain in not more than 50 words.

State against each observation below whether it is true or false. Give reasons for your answer.
i. The angular momentum of an artificial satellite rotating about the earth under its gravitation
varies with time
ii. An alpha particle scattered from an atomic nucleus moves in a plane.
iii. An artificial satellite moves at greater speed when it is nearer the earth.

Obtain an expression for the time period of a satellite orbiting the earth. A space shuttle is in a
circular orbit at a height of 250 km from the earth’s surface, where the acceleration due to earth’s
gravity is 0.93 g. Calculate the period of its orbit. Take g = 9.8 ms−2 and the radius of the earth
R = 6.37 × 106m.

A circular disc rotates on a thin air film with a period of 0.3 s. Its moment of inertia about its axis
of rotation is 0.06 kg m2. A small mass is dropped onto the disc and rotates with it. The moment
of inertia of the mass about the axis of rotation is 0.04 kg m2. Determine the final period of the
rotating disc and mass.

Derive an expression relating impulse and linear momentum. In a safety test, a car of mass
1000 kg is driven into a brick wall. Its bumper behaves like a spring (k = 5 × 106 Nm−1) and is
compressed by a distance of 3 cm as the car comes to rest. Determine the initial speed of the car.

A plane is flying with a constant speed along a straight line at an angle of 30° with the horizontal.
The weight of the plane is 80, 000 N and its engine provides a thrust of 100, 000 N in the
direction of flight. Two additional forces are exerted on the plane: the lift force perpendicular to
the plane’s wings, and the force due to air resistance opposite to the direction of motion. Draw
the free-body diagram showing all forces on the plane. Determine the lift force and the force due
to air resistance.