Related Questions

A disc is a spinning with an angular velocity $$\omega $$ rad/s about the axis of spin. The couple applied to the disc causing precession will be (where $$I$$ = Mass moment of inertia of the disc and $$\omega {\text{P}}$$  = Angular velocity of precession of the axis of spin)
A $$\frac{1}{2}I{\omega ^2}$$
B $$I{\omega ^2}$$
C $$\frac{1}{2}I\omega \omega {\text{P}}$$
D $$I\omega \omega {\text{P}}$$
The velocity of piston in a reciprocating steam engine is given by (where $$\omega $$ = Angular velocity of crank, r = Radius of crank pin circle, $$\theta $$ = Angle turned by crank from inner dead center and n = Ratio of length of connecting rod to the radius of crank)
A $$\omega {\text{r}}\left( {\sin \theta + \frac{{\sin 2\theta }}{{\text{n}}}} \right)$$
B $$\omega {\text{r}}\left( {\cos\theta + \frac{{\cos2\theta }}{{\text{n}}}} \right)$$
C $${\omega ^2}{\text{r}}\left( {\sin \theta + \frac{{\sin 2\theta }}{{\text{n}}}} \right)$$
D $${\omega ^2}{\text{r}}\left( {\cos\theta + \frac{{\cos2\theta }}{{\text{n}}}} \right)$$
At the instantaneous center, the velocity of the moving lamina at any instant is
A Zero
B Maximum
C Minimum
D Varying
A circular disc rotates at n rpm. The angular velocity of a circular ring of same mass and radius as the disc and to have the same angular momentum is
A n rpm
B $$\frac{{\text{n}}}{2}$$ rpm
C $$\frac{{\text{n}}}{4}$$ rpm
D 2n rpm
In a reciprocating steam engine, when the crank has turned from inner dead center through an angle $$\theta $$, the angular velocity of the connecting rod is given by
A $$\frac{{\omega \,\sin \theta }}{{{{\left( {{{\text{n}}^2} - {{\sin }^2}\theta } \right)}^{\frac{1}{2}}}}}$$
B $$\frac{{\omega \,\cos\theta }}{{{{\left( {{{\text{n}}^2} - {{\cos }^2}\theta } \right)}^{\frac{1}{2}}}}}$$
C $$\frac{{\omega \,\sin \theta }}{{{{\left( {{{\text{n}}^2} - {{\cos }^2}\theta } \right)}^{\frac{1}{2}}}}}$$
D $$\frac{{\omega \,\cos\theta }}{{{{\left( {{{\text{n}}^2} - {{\sin }^2}\theta } \right)}^{\frac{1}{2}}}}}$$
Which of the following property of the instantaneous center is correct?
A A rigid link rotates instantaneously relative to another link at the instantaneous centre for the configuration of the mechanism considered.
B The two rigid links have no linear velocity relative to each other at the instantaneous centre.
C The velocity of the instantaneous centre relative to any third link is same whether the instantaneous centre is regarded as a point on the first link or on the second rigid link.
D all of the mentioned
The instantaneous center of a rigid thin disc rolling on a plane rigid surface is located at
A the centre of the disc
B the point of contact
C an infinite distance on the plane surface
D the point on the circumference situated vertically opposite to the contact point
Instantaneous center of rotation of a link in a four bar mechanism lies on
A right side pivot of this link
B left side pivot of this link
C a point obtained by intersection on extending adjoining links
D none of the mentioned
Which is the false statement about the properties of instantaneous center?
A At the instantaneous center of rotation, one rigid link rotates instantaneously relative to another for the configuration of mechanism considered
B The two rigid links have no linear velocities relative to each other at the instantaneous center
C The two rigid links which have no linear velocity relative to each other at this center have the same linear velocity to the third rigid link
D The double center can be denoted either by O2 or O12, but proper selection should be made
When two links are connected by a pin joint, their instantaneous center lies
A On their point of contact
B At the center of curvature
C At the center of circle
D At the pin joint

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