Show that the value of co-efficient of friction is greater than `frac(1)(3) tan theta` for a cylinder rotationing in an inclined in an inclined plane without slipping.

How can you determine co-efficient of friciton by inclined plane method?

Find the value of: cos^-1(cos(frac{5pi}{3}))

Find the value of cos theta and tan theta if sin theta =-3/5 and piltthetalt3pi/2

If 4 tan theta=3 , find the value of (4 sin theta-3 cos theta)/(4 sin theta+3 cos theta) .

A car starts from rest on a half kilometer bridge. The co-efficient of friction between the tyres and road is 1. Show that one can't drive through the bridge in less than 10 sec.

(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction. (b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?

If tan theta =3/4 , find the value of cos^2 theta - sin^2 theta .

A 70 kg man stands in contact against the inner wail of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to ' remain stuck to the wall (without falling) when the floor is suddenly removed?

Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by v^2=(2gh)/ (i+k^2^l R^3 Using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.

Show that ((tan theta+sec theta-1)/(tan theta-sec theta +1))=(1+sin theta)/(cos theta) .