A constant torque of 1.56 N-m is applied to a rotating solid disk of radius 15 cm and mass 5.71 kg.
What is the angular velocity of the disk after 10 seconds?

Hint 1

Initial angular velocity w_{0} of the disc is not given. We assume it to be zero.

Final angular velocity of the disc = w = w_{0} + at

where a is the angular acceleration

and torque T = I a

Answer 1

Torque T = 1.56 Nm

Radius r = 15 cm = 0.15 m

Mass m = 5.71 kg

Time t = 10 s

Initial angular velocity w_{0} of the disc is not given. We assume it to be zero.

Final angular velocity of the disc = w = w_{0} + at

where a is the angular acceleration

and torque T = I a

where I is the moment of inertia, which for a solid disc, about an axis passing through its center and perpendicular to it is = ½ mr^{2 }

hence I = ½ x 0.15 x 0.15 x 5.71 = 0.064

hence a = 1.56 / 0.064 = 24.28

and w = 24.28 x 10 = 242.8 rad/s

Question 2

Find the moment of inertia of a drum shaped like a right circular cylinder of radius 0.156 m and mass 5.71 kg.

Hint 2

Moment of inertia I of a hollow cylinder about an axis passing through the center and perpendicular to its cross section is mr^{2}.

Answer 2

Moment of inertia I of a hollow cylinder about an axis passing through the center and perpendicular to its cross section is mr^{2}.

hence I = 5.71 x (0.156)^{2} = 0.14 kg m^{2}

Question 3

A string 1 meter long is used to whirl a . 50 kg. stone in a vertical circle.
What is the tension in the string when the stone is at the top of the circle moving at 5.0m/s.