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Consider a disk rotating in a horizontal plane with a constant angular speed “omega” about its center O.
The disk has a shaded region on one side of the diameter and an unshaded region on the other side.
When disk is in horizontal plane x-y with left half shaded and right half unshaded, two pebbles P and Q are simultaneously projected at an angle towards R.
The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disk.
(i) they land back on the disk before the disk has completed one-eighth rotation,
(ii) their range is less than half the disk radius,and
(iii)”omega” remains constant throughout.
Then where will the two pebbles land?
(All are invited to answer this)
In uniform horizontal circular motion, how are the vertical forces balanced?
Asked Arjun M Nair
If you are considering an object tied to a string and whirled with uniform speed in a horizontal plane, the object will be moving in a horizontal plane but the string has to make a certain angle with the horizontal so that the tension can be resolved in such a way that the horizontal component provides the centripetal force and the vertical component balances the weight of the body.
The motion will become almost entirely in a horizontal plane when the centripetal force is much larger than the weight of the particle.
The case of rid body structures the situation is complex, but as long as there are no vertical accelerations, the vertical components of forces will be balanced.
Comments are welcome from students and teachers WHO THINK!
When a high diver in a swimming event springs from the board and “tucks in”, a rapid spin result. Why is this?
The angular momentum of a body is the product of Moment of inertia (A measure of rotational inertia and it depends on the mass as well as distribution of mass about the axis of rotation. Farther the masses, greater will be the rotational inertia) and the angular velocity (The speed of rotation)
The angular momentum of a body remains unchanged in the absence of any external torque.
When the diver dives, he is giving his body a turning and takes off with his limbs stretched. In the stretched position, the moment of inertia is more. When he “tucks in”, the moment of inertia decreases. But since this happens without any external torque, it would result in an increase in angular velocity so as to keep the angular momentum constant.
A small rubber wheel is used to drive a large pottery wheel. The two wheels are mounted so that their circular edges touch. The small wheel has a radius of 3.5 cm and accelerates at the rate of 7.9 rad/s^2, and it is in contact with the pottery wheel (radius 23.0 cm) without slipping.
a)Calculate the angular acceleration of the pottery wheel
b)Calculate the time it takes the pottery wheel to reach its required speed of 64 rpm
Students and teacher visitors are requested to respond