


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. 



2. 

A cylindrical spaceship has a total mass
of 2000kg 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, as shown 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. 



3. 

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
τ=8Nm. 


Calculate 

a) 
the ratio K_{A}/K_{B} after 10s
of acceleration (where K represents kinetic energy) 

b) 
the ratio K_{A}/K_{B} when each wheel has
completed 5 revolutions. 



4. 

A uniform rod of length and mass m has a
moment of inertia L_{1}=6kgm^{2}
when rotated about an axis very near one end. 


What is its moment of inertia, L_{2} when rotating about
an axis through its centre? 



5. 

A solid cylinder of mass 0.5kg
is rolling (without slipping) along a horizontal surface at
3ms^{1}. 


Calculate its total kinetic energy. 



6. 
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. 