Rotational Dynamics
Help with advanced higher question:
A gyroscope consists of a spinning disc around an axis of rotation. The disc has a radius of 0.030m and a mass of 0.20kg.
The gyroscope is set in motion by wrapping a fine chord around its axle and pulling this free. The axle has a radius of 3.0mm.
A constant force of 15.0N is applied to the chord which unravels a distance of 0.50m.
Q. Show that the angular displacement of the gyroscope is 41.3 radians when the chord reaches the end of its length.
A gyroscope consists of a spinning disc around an axis of rotation. The disc has a radius of 0.030m and a mass of 0.20kg.
The gyroscope is set in motion by wrapping a fine chord around its axle and pulling this free. The axle has a radius of 3.0mm.
A constant force of 15.0N is applied to the chord which unravels a distance of 0.50m.
Q. Show that the angular displacement of the gyroscope is 41.3 radians when the chord reaches the end of its length.
(edited 5 years ago)
Original post by wifd149
Hint: angular displacement = angle = arc length/radius
Does arc length = 0.50m and radius = 0.003m
If so arc, length/radius = 0.5/0.003 = 166.7 radians
But the question tells me to show that the angular displacement is 41.3 radians
Am I using the wrong values?
Original post by skellerz
Does arc length = 0.50m and radius = 0.003m
If so arc, length/radius = 0.5/0.003 = 166.7 radians
But the question tells me to show that the angular displacement is 41.3 radians
Am I using the wrong values?
If so arc, length/radius = 0.5/0.003 = 166.7 radians
But the question tells me to show that the angular displacement is 41.3 radians
Am I using the wrong values?
No, I agree with you. Is the question quoted incorrectly? It could be asking about rotational velocity, not displacement.
Original post by RogerOxon
No, I agree with you. Is the question quoted incorrectly? It could be asking about rotational velocity, not displacement.
That's definitely the question, the next part asks for the final angular velocity. Must just be a mistake in the question?
Original post by skellerz
That's definitely the question, the next part asks for the final angular velocity. Must just be a mistake in the question?
I've not done the question, but I'd suggest that you continue with it and see what you get for the angular velocity. If it matches (with the correct units), I'd be sure that it's a mistake in the way that the answers are formatted. What answer do they give for the last part?
Original post by RogerOxon
I've not done the question, but I'd suggest that you continue with it and see what you get for the angular velocity. If it matches (with the correct units), I'd be sure that it's a mistake in the way that the answers are formatted. What answer do they give for the last part?
They only give the answer for the angular displacement question as it's a "show that" question. Can't get any other values to come anywhere near 41.3 either... very strange.
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