Classical Mechanics
# Circular Motion

A cyclist is riding a bicycle of wheel radius \(r\) along the edge of a rotating disk of radius \(R\, (>r)\) in such a way that he appears to be stationary to a person standing on the ground.

If the tires of the bicycle don't slip on the disk (that is, the contact points of the wheel and the disk have equal velocities), then which will have a greater rotating speed?

**Clarification:** The "rotating speed" is the angular speed (or the magnitude of the angular velocity) given by the rate of change of \(\theta\) with respect to the axis about which it is rotating:

\(\omega = \dfrac{d\theta}{dt}\)

**decrease** the chance of the bus toppling?

A bike moves at a rate of \(\si{18\ \kilo\meter/\hour}\). The rear tire has a diameter of \(\si{70\ \centi\meter}\) and has a toothwheel of diameter \(\si{7\ \centi\meter}\). The sprocket (the gear that's turned by the pedals) has diameter \(\si{20\ \centi\meter}\). Both gears are connected by the chain and there is no slippage between the chain and either gear. Under these conditions, how many times do the pedals revolve per minute?

In this matter, assume \(\pi = 3\).

Two generals, Adam and Terry, aim their long range cannons at a third general Tina. Each general calibrates the explosive power of their cannon so it will hit Tina's base using the least energy possible. Tina's base is an equal distance (along the surface of the Earth Earth) from Adam and Terry.

If the positions of Adam and Terry are as shown above, which general will need to launch their cannon rounds at a smaller speed in order to hit Tina?

**Assumptions and Details**

- The Earth is perfectly spherical.
- The launch speed of either cannon is high enough that the atmosphere is negligible.

×

Problem Loading...

Note Loading...

Set Loading...