Question 11.Q.5: Bodies in planar motion Decide whether the following rigid b...

Classical Mechanics

Bodies in planar motion

Decide whether the following rigid bodies are in planar motion: (i) a cotton reel rolling on a table, (ii) the Earth, and (iii) a snooker ball rolling after being struck with ‘side’. [If you don’t know what this means, get a player to show you.]

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

Related Answered Questions

Question: 11.2

Total moment of gravity forces A system S moves under uniform gravity. Show that the total moment of the gravity forces about any point is the same as if all the mass of S were concentrated at its centre of mass. ...

Verified Answer:

Without losing generality, let the point about whi...

Question: 11.3

Calculating the angular momentum of a particle The position of a particle P of mass m at time t is given by x = aθ², y = 2aθ, z = 0, where θ = θ (t). Find the angular momentum of P about the point B(a, 0, 0) at time t. ...

Verified Answer:

The position vector of the particle relative to B ...

Question: 11.4

Particle sliding inside a bowl A particle P of mass m slides on the inside surface of an axially symmetric bowl. Find its angular momentum about its axis of symmetry in terms of the coordinates ρ, Φ shown in Figure 11.3. ...

Verified Answer:

In order to express

L _{O} \cdot k

...

Question: 11.6

Rigid body moving under uniform gravity A rigid body is moving in any manner under uniform gravity. Show that its motion relative to its centre of mass is the same as if gravity were absent. ...

Verified Answer:

Under uniform gravity, the total moment of the gra...

Question: 11.12

A circus trick In a circus trick, a performer of mass m causes a large ball of mass M and radius a to accelerate to the right (see Figure 11.12) by running to the left on the upper surface of the ball. The man does not fall off the ball because he maintains this motion ...

Verified Answer:

Suppose the motion is planar and that, at time t, ...

Question: 11.14

Leaning rod A rough floor lies in the horizontal plane z = 0 and the plane x = 0 is occupied by a smooth vertical wall. A uniform rod of mass M has its lower end on the floor at the point (a, 0, 0) and its upper end rests in contact with the wall at the point (0, b, c). ...

Verified Answer:

The external forces acting on the rod are the norm...

Question: 11.13

Leaning panel A rectangular panel ABCD of mass M is (rather carelessly) placed with its edge AB on the rough horizontal floor z = 0 and with the vertex D resting against the smooth wall x = 0, as shown in Figure 11.13. The four vertices of the panel ...

Verified Answer:

The external forces acting on the panel are the no...

Question: 11.11

The cotton reel problem A cotton reel is at rest on a rough horizontal table when the free end of the thread is pulled horizontally with a constant force T , as shown in Figure 11.11. Given that the reel undergoes planar motion,* how does it move? ...

Verified Answer:

Suppose the ends of the reel have radius a, the ax...

Question: 11.10

Planar motion: mass hanging from a pulley A circular pulley of mass M and radius a is smoothly pivoted about the axis {O, j}, as shown in Figure 11.10. A light inextensible string is wrapped round the pulley so that it does not slip, and a particle ...

Verified Answer:

This problem is most easily solved by using energy...

Question: 11.Q.4

Form of the motion This is all very well, but what does the motion actually look like? ...

Verified Answer:

Despite the problem being called integrable, the i...