20f7: A 4kg circular ring, shown in the figure, rolls down the inclined plane without slipping with an initial angular velocity of 10 rad/s @ s=0. Find the translational and angular velocity of the ring after it has traveled the distance s = 2m. μ = 0.25, k = 0.2. For a ring: IG : mr². =

consider the slider-crank mechanism shown. Crank AB is 3.00 m long. Rod BD is 2.00 m long. The velocity at point B is 6.00 m/s, ↘45.0°. a. speed of the piston at D? b. On which area is the instantaneous center of rod AB located?

Consider the disk and axle shown below. The axle has a constant angular velocity (in rad/s) in the inertial frame given by: A/N = 0.152 i. The disk has an angular velocity (in rad/s) in the axle frame given by: p/A 0.504 k . Calculate the magnitude of angular acceleration of the disk in the inertial frame (in rad/s?). N D

Consider a toy vehicle with a body of mass M = 2Kg on two wheels, each of mass m = 1Kg and radius r = 0.1 m as shown in the figure. It starts from rest on top of a small hill of height H = 10 m and rolls without slipping. What is the linear velocity of the center of mass at the bottom of the hill? HINT: There is rotational and translational kinetic energy in this problem. Vo = 0 M- Vf M-2K m=lKg molky

-10 10 40 a. Find the volume of the parallelepiped whose edges are represented by A = 2i - 3j + 4k, ii. B = 1+ 2) - k, C = 31 - 1 + 2k . b. The angular velocity of a rotating rigid body about an axis of rotation is given by ai = 4i +j - 2k. Find the linear velocity of a point P on the body whose position vector relative to a point on the axis of rotation is 2i-3j+k. ii. Find the moment of inertia tensor from the given picture. 300 mm P.T.O. iv. Given point P = (1, -2, 3) and vector A = yz i+x1- yx k , express this vector in cylindrical coordinate system. V. a. Show that the contraction of the outer product of the tensors AP and B, is an invariant. b. Show that every tensor can be expressed as the sum of two tensors, one of which is symmetric and the other skew-symmetric in a pair of covariant or contra variant indices. vi. The 4-oz top with radius of gyration about its spin axis of 0.62 in. is spinning at the rate p = 3600 rev/min in the sense shown, with its spin axis making an angle…

A 21 mm diameter glass marble with a mass of 25 g rolls without slipping down a track toward a vertical loop of radius R=15 cm, as shown in the figure. Approximate the minimum translational speed vmin the marble must have in order to complete the loop without falling off the track when it is a height H=25 cm above the bottom of the loop. H R Figure is not to scale.

Az Ay α = 0 A || y Eat Ice Cream X kg An advertisement can be modelled as a thin plate with uniform density distribution, p = 80 If the m² supporting wire at B suddenly snaps, what is the angular acceleration of the advertisement and the reaction forces at A at that instant? The sign has a width = 2 m and a height h = 1.5 m. Force directions should match the x and y directions on the image XN N rad W CW B h UBC Engineering