Get Advice on Live Video Call
Earn $ Cash $ with
consultations on Bissoy App

A disc spinning on its axis at 20 rad/s will undergo precession when a torque 100 N-m is applied about an axis normal to it at an angular speed, if mass moment of inertia of the disc is the 1 kg-m2

Correct Answer: 5 rad/s
Gyroscopic couple acting on the disc, C = I. ω. ωp 100 = 1 . 20. ωp ωp = 100/1.20 = 5 rad/s

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 disc is spinning with an angular velocity? rad/s about the axis of spin. The couple applied to the disc causing precession will be

A disc is a spinning with an angular velocity ω rad/s about the axis of spin. The couple applied to the disc causing precession will be

The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$    A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.
Classical Mechanics mcq question image
The moment of inertia of the resulting body about Y-axis is

A disc is rotating with ω =10rad/s about a fixed central axis which is perpendicular to its plane. The disc has a mass =2kg & radius =10cm. A small particle of mass 100gm is put slowly on the disc’s outer circumference. There is sufficient friction between the disc and the particle. What will be the new angular velocity of the system?

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)

The moment of inertia of a uniform circular disc about its diameter is 100 gcm2. What is its moment of inertia about an axis perpendicular to its plane.

The moment of inertia of a planar disc about a diameter is 8kgm2. What is the moment of inertia about an axis passing through its centre and perpendicular to the plane of disc?

An electric motor drives a machine through a speed reducing gear of ratio 9:1. The motor armature, with its shaft and gear wheel, has moment of inertia 0.6 kg-m2. The rotating part of the driven machine has moment of inertia 45 kg-m2. The driven machine has resisting torque of 100 N-m and the efficiency of reduction gear is 95%. Find the power which the motor must develop to drive the machine at a uniform speed of 160 r.p.m.

A connecting rod of mass 5.5 kg is placed on a horizontal platform whose mass is 1.5 kg. It is suspended by three equal wires, each 1.25 m long, from a rigid support. The wires are equally spaced round the circumference of a circle of 125 mm radius. When the c.g. of the connecting rod coincides with the axis of the circle, the platform makes 10 angular oscillations in 30 seconds. Determine the mass moment of inertia about an axis through its c.g.