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A Question from Rotational Mechanics

A thin spherical shell lying on a rough horizontal surface is hit by a cue in such a way that the lines of action passes through the centre of shell. As a result the shell starts moving with a linear speed ‘V’ without any initial angular velocity. Find the linear speed of the shell after it starts pure rolling on surface.

Asked Raj

 

A thought provoking (HOTS) problem from rotation

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.

Assume that

(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)

Uniform Circular Motion in Horizontal Plane

In uniform horizontal circular motion, how are the vertical forces balanced?

Asked Arjun M Nair

Answer:

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.

Refer:

http://cnx.org/content/m14090/latest/

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!

Physics of Diving

When a high diver in a swimming event springs from the board and “tucks in”, a rapid spin result. Why is this?

Answer: This is the consequence of conservation of angular momentum.

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.

Stacked Spinning Discs Problem

Ryan asks:

“If I stack up a spinning disc on another spinning
disc. What will be the spinning RPM of the top
disc from a person’s eye on side ?”

What is torsion?

Paul asked:

What is torsion?

Answer:
Torsion means the twisting of an object due a torque applied on it.

Also defined as the deformation caused when one end of an object is twisted in one direction and the other end is held motionless or twisted in the opposite direction.

Question from Rotational Dynamics

Dyana Asked:

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

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