Question

A grinding wheel of mass 5.0kg and diameter 0.4m is rotating with an angular speed of 2 rev s-1. Calculate the torque which will increase its angular speed to 8 revolution per second in2s.

Answer 1

mass of grinding wheel , m=5 kg

diameter of grinding wheel= 0.4 m

initial angular velocity, w1= 2 rev/sec

final angular velocity,w2=8 rev/sec

time interval from initial to final velocity,t= 2 secs

torque= rotational inertia*angular acceleration

T= I*Alpha

Alpha, angular acceleration= w2-w1/t

Alpha= 3 rev/sec^2

rotational inertia= 0.5*m*r^2

I=2.5*0.04

I=0.1 kgm^2

therefore torque equals= 0.3 N.m

Answer 2

A wire of length L and area of cross-section A is held straight between two rigid supports It has zero stress at 0° C. Show that the stress in the wire at 100°C is 100 aY, where a is coefficient of linear expansion and Y is young's modulus of elasticity of the wire.