for the yoyo , force equation in vertical direction is given as
mg - T = ma
T = mg - ma eq-1
Torque equation is given as
T r = I a/r
(mg - ma) = (mr2) (a/r2)
2 ma = mg
a = g/2
a = 4.9
A cylinder of mass M and radius R is rotting down an incline with angle theta....
A cylinder of mass M and radius R is rolling down an incline with angle theta. Find the acceleration of the cylinder as it rolls down the incline. Find the acceleration a and the tension T in the string of a yo-yo when it is released.
2. A uniform, solid cylinder with mass M and radius 2R is on an incline plane with angle of inclination of 6. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the...
a yo yo of mass m and outer radius R rolls down a string on an axle of radius R0. The moment of inertia for the yoyo about its center of mass is Icm. Find the acceleration pf the yo-yo's center of mass ad it rolls down the string. draw as point particle.
A very thin circular hoop of mass(m) and radius(r) rolls without slipping down a ramp inclined at an angle(theta) with the horizontal, as shown in the figure.What is the acceleration(a) of the center of the hoop? Express your answer in terms of some or all of the variablesm,r, theta, and the magnitude of the acceleration due to gravity(g).
A solid cylinder of radius 12.0 cm rolls down an incline with slipping. The angle of the incline is 28°. The coefficient of kinetic friction on the surface is 0.370. What is the angular acceleration (in rad/s2) of the solid cylinder? (Enter the magnitude.) rad/s2 What is the linear acceleration (in m/s2)? (Assume v > ωr. Enter the magnitude.) m/s2
A hollow cylinder is released from rest and rolls down the incline without slipping. The incline has an angle of thera=40 degrees with the horizontal. The mass and radius of the cylinder is M=5kg and R=0.55m respectively. Moment of inertia of a hollow cylinder is I=MR^2. a)Draw the free body diagram of the hollow cylinder showing all the forces and their components. b) Using newtons 2nd law for linear and rotational motion, derive an expression for linear acceleration of the...
A
uniform sphere rolls down an incline. (a) What should be the
incline angle theta if the linear acceleration of the center of the
sphere is to be 0.2g, where g is acceleration due to gravity? (b)
For this angle, what would be the acceleration of a frictionless
block sliding down the incline?
A uniform sphere('a = žmR”, rolls down an incline.(a) What should be the incline angle if the linear acceleration of the center of the sphere is to...
A solid sphere of mass M and radius R sits on a an incline of angle θ, when it is let go it rolls down-hill without slipping at total vertical distance of h. At the bottom of the hill the ball moves onto a horizontal surface and enters into a completely elastic collision with a stationary block of height 2R and mass 2M. Find the speed of the block right after the collision.
torque on a cylinder
Cylinder drop (2) A uniform cylinder of mass m - 2 kg. radius r = 0. 1 m (and I = 1/2mr^2) has a massless, frictionless string wrapped around the outside, and is subsequently dropped from rest. The cylinder will fall and the string will unwind like a yo-yo. The string will haw some tension T during this process. Find the net force acting on the cylinder (in terms of T if necessary). Find the net...
A yo-yo can be modelled as a cylinder with radius r and mass m
(I = ½mr2). While hanging at the bottom of a string, the yo-yo is
given initial upward velocity and initial rotational velocity, and
as it moves upward the string is wrapped around the cylinder (for
simplicity, assume the string wraps around the full radius).
Determine the tension in the string as the yo-yo moves upward.
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