#2. [Swinging Disk] A uniform circular disk of mass M and radius R is set swinging...
2. As shown below a uniform disk of radius R 10.0 cm and mass M 0.850 kg is attached to the end of a uniform rigid rod of length L = 500 mm and mass m = 0.210 kg. Take positive θ in the counterclockwise direction, and positive angular velocity ω as into the page. Assume small angle deflection (a) When the disk is suspended from a pivot as sown what is the period of its motion? (b) If this...
Please show all work with algebra. disk 5. A uniform disk of mass M and radius R is suspended from an axle at its rim, as (a) (9 points) Draw a free body diagram for the disk when it is pulled out by a (b) (9 points) Write out the torque equation for small oscillations of the disk about shown in the figure below. It is then pulled out by a small angle and released small angle. its equilibriumi position...
The Physical Pendulum. A pendulum is formed by hanging a 60cm long stick of mass m from a pivot, as shown at left. Find the angular acceleration of the pendulum when the pendulum is displaced by a small angle θ, and show that the motion is simple harmonic motion in the limit of small oscillations. Find the period of the pendulum in this limit.
A pendulum consists of a disk of mass, m, and radius, r, connected to a pivot point via string (of negligible mass) of length, l. Note, the disk hangs vertically and the string is attached to its top. For small angles, derive an expression for: (a) angular position as a function of time (b) angular velocity as a function of time (c) angular acceleration as a function of time
A uniform disk with mass m = 9.07 kg and radius R = 1.36 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 313 N at the edge of the disk on the +x-axis, 2) a force 313 N at the edge of the disk on the –y-axis, and 3) a force 313 N acts at the edge of the disk at an angle θ =...
A pendulum consists of a uniform rod of total mass m and length L that can pivot freely around one of its ends. The moment of inertia of such a rod around the pivot point is 1/3mL^2 The torque around the pivot point of the pendulum due to gravity is 1/2mgLsinθ, where θ is the angle the rod makes with the vertical and g is the acceleration due to gravity. a) Write down the equation of motion for the angle...
A uniform disk of radius 0.455 m0.455 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with the same mass as the disk is attached around the disk's rim. A tangential force of 0.237 N0.237 N applied at the rim causes an angular acceleration of 0.129 rad/s2.0.129 rad/s2. Find the mass of the disk.Why is this wrong? A uniform disk of radius 0.455 m and unknown mass is constrained to rotate about...
A uniform disk with mass m = 9.04 kg and radius R = 1.35 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 309 N at the edge of the disk on the +x-axis, 2) a force 309 N at the edge of the disk on the –y-axis, and 3) a force 309 N acts at the edge of the disk at an angle θ =...
A uniform disk of radius 0.461 m and unknown mass is constrained to rotate about a perpendicular axis through its center. A ring with the same mass as the disk is attached around the disk's rim. A tangential force of 0.243 N applied at the rim causes an angular acceleration of 0.123 rad/s2. Find the mass of the disk. mass of disk:
Consider a uniform disk of radius R and mass m sliding down an incline making an angle θ with respect to the horizontal. The coefficient of kinetic friction between the disk and the surface is μk. The torque due to friction causes the disk to rotate as it slides down the incline. a) Compute the linear acceleration of the disk as it slides down the incline. b) Compute the angular acceleration of the disk as it slides down the incline....