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# Yo-yo speed and energy; angular speed of a bicycle wheel

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A yo-yo has a rotational inertia of 1180 g·cm2 and a mass of 148 g. Its axle radius is 3.58 mm, and its string is 139 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed?

With axle and spokes of negligible mass and a thin rim, a certain bicycle wheel has a radius of 0.350 m and weighs 36.0 N; it can turn on its axle with negligible friction. A man holds the wheel above his head with the axle vertical while he stands on a turntable that is free to rotate without friction; the wheel rotates clockwise, as seen from above, with an angular speed of 53.0 rad/s, and the turntable is initially at rest. The rotational inertia of wheel + man + turntable about the common axis of rotation is 2.50 kg·m2. The man's free hand suddenly stops the rotation of the wheel (relative to the turntable). (a) Determine the resulting angular speed of the system. (b) Is the direction of the rotation: 1 - clockwise or 2 - counterclockwise? Give the number of the correct answer.

https://brainmass.com/physics/angular-momentum/speed-energy-angular-speed-bicycle-wheel-303112

#### Solution Preview

A yo-yo has a rotational inertia of 1180 g·cm2 and a mass of 148 g. Its axle radius is 3.58 mm, and its string is 139 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed?

Solution:

T
M = 148 g
I = 1180 g.cm2
r = 0.358 cm
Mg

a) Forces acting on the yo-yo are shown in the fig.. Weight Mg acts vertically downwards at the centre of mass and ...

#### Solution Summary

The yo-yo speed and energy and angular speed of a bicycle wheel is examined.

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