Rock whirling in vertical circle

[nrc_8706]

a rock whirls in a vertical circle of radius 8m. acceleration of gravity 9.8m/s^2

what must the speed be to have tangential=radial acceleration when the string makes a 37 angle with respect to the vertical?

is it Wsinangel=ma

v=Wsinangle*r/m)^1/2 ?

 

[Fermat]

If W is mg, then yes.

v² = gr.sin@

 

[quicknote]

I can confirm that the equation for tangential acceleration in this scenario is v = Wsin(angle) * r/m^1/2, where v is the speed, W is the angular velocity, angle is the angle with respect to the vertical, r is the radius, and m is the mass of the object. This equation can be derived from the formula for centripetal acceleration, a = v^2/r, by substituting in the value for centripetal acceleration (gravity in this case) and solving for v. Therefore, the speed needed to have tangential and radial acceleration in equilibrium would be v = (9.8m/s^2 * 8m)^1/2 / sin(37) = 15.37 m/s. This means that the rock must be moving at a constant speed of 15.37 m/s in order to maintain a circular motion with both tangential and radial acceleration.