Question

A bike is moving on a curved flat road of radius 200 m with a speed of 25 m/s. The combined moment of inertia of the rotating masses is 16 kg-m2. Consider rotating masses of the engine have an angular speed of 50 rad/s in clockwise direction when viewed from the front of the bike. Find the magnitude of the gyroscopic moment.
A. 150 Nm
B. 125 Nm
C. 100 Nm
D. 75 Nm

Answer 1

Given:

A bike is moving on curved flat of radius 200 m with a speed of 25 $\frac{m}{s}$ .

Moment of Inertia = 16 $kg m^{2}$

Angular speed of masses = 50 $\frac{rad}{s}$ in clockwise direction.

To Find:

Magnitude of gyroscopic moment

Solution:

A gyroscope is a device used to measure orientation and angular velocity.

If a body is rotating about a axis.If this axis start rotating with respect to a plane, a torque is applied on the rotating mass.

To restore the position of the mass, a restoring couple acts on the mass, this reaction or restoring torque is called gyroscopic couple.

It is defined by the equation;

$T = Iww'^{2}$

$w' = \frac{V}{R}\\\\\\w'= \frac{25}{200}$

$w= 50 \frac{rad}{s}$

I = 16 kg $m^{2}$

$T = (16)(50)((\frac{25}{200}) ^{2} )\\T = 125Nm$

Magnitude of gyroscopic moment is 125 Nm.