Question 1
A motor produces a torque of 5Nm. It is used to accelerate a wheel of radius 10cm and moment of inertia 2kgm^{2} which is initially at rest. Calculate  
a)  the number of revolutions made by the wheel in the first 5s 
b)  the angular velocity after 5s 
c)  the centripetal acceleration of a point on the rim of the wheel after 5s. 
A cylindrical spaceship has a total mass of 2000 kg and a diameter of 2·5m. The spaceship is rotating with an angular velocity of 0·4rads^{1}. Two rockets are used to stop the rotation. See diagram below. 
If each rocket provides a constant force of 50N, how long will it take to stop the rotation? 
(For simplicity, consider the spaceship to be a thinwalled cylinder with all the mass concentrated in the walls.) 
Two wheels have the same mass, m. Wheel A has radius r_{a} = 10cm and is a uniform, solid wheel. Wheel B has radius r_{b} = 15cm and has all its mass concentrated in a thin rim (something like a bicycle wheel). Both wheels are caused to accelerate from rest by a torque = 8Nm. Calculate  
a)  the ratio (K.E. of A)/(K.E. of B) after 10s of acceleration 
b) 
the ratio (K.E. of A)/(K.E. of B) when each wheel has completed 5 revolutions. (The wheels will, of course, take different times to complete 5 revolutions, but this has no relevance to this part of the question.)

A uniform rod of length and mass m has a moment of inertia I_{1} = 6kgm^{2} when rotated about an axis very near one end. What is its moment of inertia, I_{2}, when rotating about an axis through its centre? 
A solid cylinder of mass 0·5kg is rolling (without slipping) along a horizontal surface at 3ms^{1}. Calculate its total kinetic energy. 
a)

State the law of conservation of angular momentum.

b)

Use this law to explain how an iceskater can change his/her angular velocity.

c)

Halley’s comet has a very eccentric orbit around the sun; that is, the ratio, furthest distance from the sun (aphelion) to nearest distance to the sun (perihelion), is large. At aphelion, it is about 4.8 × 10^{9}km and at perihelion it is only about 8.8 × 10^{7}km from the sun. At aphelion, its speed is about 5.3 × 10^{3}ms^{1}. Use the principle of conservation of angular momentum to calculate its speed at perihelion.
