Question 1
| 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. |
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| 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 |
| 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.)
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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. |
a)
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State the law of conservation of angular momentum.
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b)
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Use this law to explain how an ice-skater can change his/her angular velocity.
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c)
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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.
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