2 and 3 Dimension Motion Circular Motion Gravitation Force
Question 1
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 w0 of the disc is not given. We assume it to be zero.
Final angular velocity of the disc = w = w0 + 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 w0 of the disc is not given. We assume it to be zero.
Final angular velocity of the disc = w = w0 + 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 mr2
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.
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.
