Subjective Type

Suppose that yo-yo in Problem $$17$$, instead of rolling from rest, is thrown so that its initial speed down the string is $$1.3\ m/s$$.What is the linear speed?

Solution

As it reaches the end of the string, its center of mass velocity is given
$$v_{com}=v{com.0}+a_{com}t=v_{com.0}-\dfrac{gt}{1+I_{com}/MR_0^2}$$
Thus, we obtain
$$v_{com}=-1.3 m/s-\dfrac{(9.8\ m/s^2)(0.885\ s)}{1+\dfrac{0.000095\ kg.m^2}{(0.12\ kg)(0.0032\ m)^2}}$$
so its linear speed at that moment is approximately $$1.4\ m/s.$$

SIMILAR QUESTIONS

Rotational Dynamics

An imperfectly rough sphere moves from rest down a plane inclined at an angle $$\alpha$$ to the horizontal. The coefficient of friction between the inclined plane and sphere is $$\mu$$. Then:

Rotational Dynamics

the magnitude of the friction coefficient at which slipping is absent;

Rotational Dynamics

how long the cylinder will move with sliding;

Rotational Dynamics

In the figure, a solid brass ball of mass $$0.280\ g$$ will roll smoothly along a loop track when released from rest along the straight section. The circular loop has radius $$R=14.0\ cm$$ and the ball has radius $$r << R$$. What is $$h$$ id the ball is on the verge of leaving the track when it reaches the top of the loop?

Rotational Dynamics

In figure, a solid brass ball of mass $$0.280\ g$$ will roll smoothly along a loop the loop truck when released from rest along the straight section. The circular loop has radius $$R=14.0\ cm$$ and the ball has radius $$r << R$$. What is $$h$$ id the ball is on the verge of leaving the track when it reaches the top of the loop? If the ball is released at height $$h=6.00\ R$$, what are the direction of the horizontal force component acting on the ball at point $$Q$$?

Rotational Dynamics

A uniform wheel of mass $$10.0\ kg$$ and radius $$0.400\ m$$ is mounted rigidly on a massless axle through its center. The radius of the axle is $$0.200\ m$$, and the rotational inertia of the wheel-axle combination about its central axis is $$0.600\ kg.m^2$$.The wheel is initially at rest at the top of a surface that is inclined at angle $$\theta =30.0^{o}$$ with the horizontal; the axle rests on the surface while he wheel extends into a groove in the surface without touching the surface. Once released, the axle rolls down along he surface smoothly and without slipping. When the wheel-axle combination has moved down the surface by $$2.00\ m$$, what are its rotational kinetic energy?

Rotational Dynamics

A hexagonal pencil placed on an in clined plane with a slope $$\alpha$$ at right angles to the generatrix (i.e. the line of intersection of the plane and the horizontal surface) remains at rest. The same pencil placed parallel to the generatrix rolls down the plane.Determine the angle $$\phi$$ between the axis of the pencil and the generatrix of the inclined plane $$(Fig.46)$$ at which the pencil is still in equilibrium.

Rotational Dynamics

An inclined plane makes an angle of $$60^o$$ with horizontal. A disc rolling down this inclined place without slipping has a linear acceleration equal to:

Rotational Dynamics

Which of the following order is true for final $$KE$$ of the bodies?

Rotational Dynamics

Which of the following order is true for time taken by the bodies to reach the bottom of incline?

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