(a) Starting from I = | r² dm, show that the moment of inertia of a uniform cylinder of mass M and radius R (spinning about its central axis) is given by I MR² 2 (b) A cart has four wheels, each a uniform disc of mass 1 kg and radius 0.5 m. The body of the cart has a mass of 6 kg. What is the total moment of inertia of the cart as it rolls down a slope? (c) The cart starts from rest and rolls down a slope a vertical distance of 5 m. How fast is it then travelling? [Ignore friction and air resistance.]
(a) Starting from I = | r² dm, show that the moment of inertia of a uniform cylinder of mass M and radius R (spinning about its central axis) is given by I MR² 2 (b) A cart has four wheels, each a uniform disc of mass 1 kg and radius 0.5 m. The body of the cart has a mass of 6 kg. What is the total moment of inertia of the cart as it rolls down a slope? (c) The cart starts from rest and rolls down a slope a vertical distance of 5 m. How fast is it then travelling? [Ignore friction and air resistance.]
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![(a) Starting from I = [r² dm, show that the moment of inertia of a uniform cylinder of mass
M and radius R (spinning about its central axis) is given by I =
MR²
2
(b) A cart has four wheels, each a uniform disc of mass 1 kg and radius 0.5 m. The body of the
cart has a mass of 6 kg. What is the total moment of inertia of the cart as it rolls down a slope?
(c) The cart starts from rest and rolls down a slope a vertical distance of 5 m. How fast is it
then travelling? [Ignore friction and air resistance.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda2446de-d306-47c9-ac9b-78bc0bd623aa%2F74db64df-9a68-4ac7-9df0-f34d91782138%2F2sqwnv_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Starting from I = [r² dm, show that the moment of inertia of a uniform cylinder of mass
M and radius R (spinning about its central axis) is given by I =
MR²
2
(b) A cart has four wheels, each a uniform disc of mass 1 kg and radius 0.5 m. The body of the
cart has a mass of 6 kg. What is the total moment of inertia of the cart as it rolls down a slope?
(c) The cart starts from rest and rolls down a slope a vertical distance of 5 m. How fast is it
then travelling? [Ignore friction and air resistance.]
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