Question

Two wheels have the same mass and radius of 4.1 kg and 0.37 m, respectively. one has (a) the shape of a hoop and the other (b) the shape of a solid disk. the wheels start from rest and have a constant angular acceleration with respect to a rotational axis that is perpendicular to the plane of the wheel at its center. each turns through an angle of 14 rad in 8.7 s. find the net external torque that acts on each wheel.

Answer 1

Since the wheel start from rest. angular acceleration, θ=1/2αt² 14=1/2α x 8.7² α= 0.3699 rad/s² moment of inertia of loop= mr²= 4.1x0.37=1.517 kgm² torque=T= lα T= 0.5611Nm= 0.56Nm to significant figure Disc moment of inertia of disc= 1/2mr² Required torque value= 0.28Nm So, I= 1/2X 4.1X 0.37²= 0.280 Kgm² T= Iα = 0.280 X 0.3699= 0.10 to two significant figure