|A motor produces a torque of 5Nm. It is used to accelerate a wheel of radius 10cm and moment of inertia 2kgm2 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 space-ship has a total mass of 2000 kg and a diameter of 2·5m. The space-ship 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 space-ship to be a thin-walled cylinder with all the mass concentrated in the walls.)|
|Two wheels have the same mass, m. Wheel A has radius ra = 10cm and is a uniform, solid wheel. Wheel B has radius rb = 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|
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 I1 = 6kgm2 when rotated about an axis very near one end. What is its moment of inertia, I2, 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.|
State the law of conservation of angular momentum.
Use this law to explain how an ice-skater can change his/her angular velocity.
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 × 109km and at perihelion it is only about 8.8 × 107km from the sun. At aphelion, its speed is about 5.3 × 103ms-1. Use the principle of conservation of angular momentum to calculate its speed at perihelion.