Question

The rotation of rod ( O A ) about ( O ) is defined by the relation ( heta=t^{3}-4 t ), where ( heta ) and ( t ) are expressed in radians and seconds, respectively. Collar ( B ) slides along the rod so that its distance from ( O ) is ( r=2.5 t^{3}-5 t^{2} ), where ( r ) and ( t ) are expressed in inches and seconds, respectively. When ( t=1 mathrm{~s} ), determine (a) the velocity of the collar, (b) the acceleration of the collar, and (c) the radius of curvature of the path of the collar.

          The rotation of rod ( O A ) about ( O ) is defined by the relation ( 	heta=t^{3}-4 t ), where ( 	heta ) and ( t ) are expressed in radians and seconds, respectively. Collar ( B ) slides along the rod so that its distance from ( O ) is ( r=2.5 t^{3}-5 t^{2} ), where ( r ) and ( t ) are expressed in inches and seconds, respectively. When ( t=1 mathrm{~s} ), determine (a) the velocity of the collar, (b) the acceleration of the collar, and (c) the radius of curvature of the path of the collar.

The rotation of rod ( O A ) about ( O ) is defined by the relation ( heta=t^3-4 t ), where ( heta ) and ( t ) are expressed in radians and seconds, respectively. Collar ( B ) slides along the rod so that its distance from ( O ) is ( r=2.5 t^3-5 t^2 ), where ( r ) and ( t ) are expressed in inches and seconds, respectively. When ( t=1 mathrm s ), determine (a) the velocity of the collar, (b) the acceleration of the collar, and (c) the radius of curvature of the path of the collar.

Added by Marissa B.

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