Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

PHYS101: Dynamics and Relativity

Problem Sheet 4

Formative questions (unassessed)

1) An object rotates around a rotation axis with an initial angular velocity of ω0 = 0.2 rad/s. The object experiences a constant angular acceleration α = −π/2 rad/s2.

(a) How much time does the object take to come to rest?

(b) What angle will the object have rotated through by the time it comes to rest?

2) Consider a pulley with a rope wound around it. A block of mass m is fastened to one end of the rope. The other end of the rope is fastened to the pulley (which can be considered as a thin disk of radius r). The block is released from rest, which starts the pulley rotating.

(a) Calculate the torque exerted on the pulley.

(b) Calculate the work done in rotating the pulley by two revolutions, if m = 100 g and r = 10 cm.

Assessed question for classwork session

3) Four spheres, all of radius ?, are arranged as shown below. Two spheres, of masses m1, are centred at x1 = 0 but offset by 2 units in y. Two spheres, of masses m2, are centred at x2 and similarly offset in y. A rotation axis passes through the x- position of the centre-of-mass of the four spheres, and the system rotates about this.

(a) Derive an expression for the position of the centre of mass. [2]

(b) The moment of inertia of a solid sphere of mass m and radius r about a rotation axis passing through its centre of mass is I = 2/5mr2. Show that the moment of inertia of the four sphere system about the rotation axis is

[4]

(c) The system rotates twice a minute. Calculate the angular momentum of the system, if x2 = 10 m, r = 0.2 m and m2 is twice as large as m1 (m2 = 5 kg). [3]

(d) Would you expect the angular momentum to be larger or smaller if the rotation axis is moved to halfway between the spheres (ie to x2/2), assuming the same rotation rate? Explain your answer. [3]